Read from book

• sections 7.1 to 7.8 and the lecture

Content

1. Firm’s decision
2. Breakfast cereal: Choosing a price
   • demand curve, price, isocost
3. Economies of Scale
4. Production: The cost function for beautiful cars
5. Demand and Isoprofit
6. Profit maximization using marginal revenue and marginal cost

1. Firm’s decision

• Objective: Is to maximize profit.

• profit = revenue - cost \((\pi = p \times q - C)\)

• A firm’s success depends on:
  • price and quantity
  • ability to attract customers
  • produce at a lower cost and higher quality
• Ways by which the firm can influence demand and cost
  • price and quantity
  • innovation (attractive products)
  • lower cost of production

• Focus on the choice of price and quantity

Some examples of a firm

• Walmart: low price strategy
  • keep the price low
  • profit margin low for each unit sold
  • but low price may attract consumers

\(~\)

• Apple: high price
  • high price for iPhones and iPads
  • increase profit by choosing large price premium
  • For example, between April 2010 and March 2012, profit per unit on Apple iPhones was between 49% and 58% of the price.

2. Breakfast cereal: Choosing a price

• To decide on what price to charge, a firm needs information about demand of a product
• consider the demand curve for Apple-Cinnamon Cheerios, introduced by General Mills in 1989 (in the next slide)

Breakfast cereal: Demand curve

Breakfast cereal: profit function

• shows the relationship between price and quantity demanded
  • For example, if price is $3 customers will demand 25,000 pounds
• If you had to choose a price for a bag of cereal, how would you do it?
• Objective is to maximize profit
• \(Total\; cost = unit\; cost \times quantity\)
  • assume that cost per unit is 2 dollars
  • \(Total\; cost = 2\times Q\)
• \(Total\; Revenue = price \times quantity\)
  • = \(P \times Q\)

• \(profit = total \; revenue - total\; cost\)

• Now, the formula for profit:
  • \(profit = (P-2) \times Q\)

Isoprofit curves as the firm’s indifference curve

• Once you have the profit function (from the previous slide), given the exact value of profit, you can find combinations of \(P\) and \(Q\) to give you that value of profit.
• For any value of profit, you can then plot the combinations of price and quantity as given in the figure below.
  

  Figure 2. Isoprofit curve for Cheerios

Question 7.1 Choose the correct answer(s)

• A firm’s cost of production is £12 per unit of output. If P is the price of the output good and Q is the number of units produced, which of the following statements is correct?

  • Point (Q, P) = (2,000, 20) is on the isoprofit curve representing the profit level £20,000.
  • Point (Q, P) = (2,000, 20) is on a lower isoprofit curve than point (Q, P) = (1,200, 24).
  • Points (Q, P) = (2,000, 20) and (4,000, 16) are on the same isoprofit curve.
  • Point (Q, P) = (5,000, 12) is not on any isoprofit curve.

Question 7.2

Question 7.2 Choose the correct answer(s)

• Consider a firm whose unit cost (the cost of producing one unit of output) is the same at all output levels. Which of the following statements are correct?

  • Each isoprofit curve depicts the firm’s profit for different outputs for a given price of the output good.
  • Isoprofit curves can be upward-sloping when at high profit levels.
  • Every price-quantity combination lies on an isoprofit curve.
  • Isoprofit curves slope downward when the price is above the unit cost.

Demand and Isoprofit curve

• if you look at the profit function \(profit = (P-2) \times Q\), you should note that profit can be increased by increasing both \(P\) and \(Q\)
• however, it is not possible to increase both \(P\) and \(Q\) simultaneously, as \(P\) increases \(Q\) is likely to fall
  • if price of something increases you are going to buy less of it
• Hence, the profit function (indifference curve of the firm) is constrained by the demand curve

Demand and Isoprofit curve

Demand and Isoprofit curve

• In Figure 3, demand curve acts as a constraint whereas isoprofit curve is the firm’s indifference curve. As a mangager, you pick price such that it maximizes your profit. Here, choosing point E, where the demand curve is tangential to the isoprofit curve, allows you to maximize profit.

• In point E, price \(P=\$4.4\) and \(Q=14,000 \;pounds\).

• The isoprofit curve is your indifference curve, and its slope at any point represents the trade-off you are willing to make between P and Q. Note that the slope of the indifference curve is also the marginal rate of substitution (MRS). The trade-off that a person is willing to make between two goods.

• The slope of the demand curve is the trade-off you are constrained to make—your MRT, or the rate at which the demand curve allows you to ‘transform’ quantity into price. You cannot raise the price without lowering the quantity, because fewer consumers will be buy a more expensive product.

Question 7.3 Choose the correct answer(s)

The table represents market demand Q for a good at different prices P. \(~\)

	X1	X2	X3	X4	X5	X6	X7	X8	X9	X10	X11
Price	Q	100	200	300	400	500	600	700	800	900	1000
Quantity	P	270	240	210	180	150	120	90	60	30	0

• The firm’s unit cost of production is £60. Based on this information, which of the following is correct?

  • At Q = 100, the firm’s profit is £20,000.
  • The profit-maximizing output is Q = 400.
  • The maximum profit that can be attained is £50,000.
  • The firm will make a loss at all outputs of 800 and above.

3. Economies of Scale

• What are some internal structures that can explain why firms like Walmart, Amazon have grown so big.

• Technological Advancement - Use fewer inputs per unit of production.
• Cost Advantages - Large firms have more bargaining power, so they can get inputs for cheaper. In a case of a large firm, fixed costs such as advertisement will contribute less to the cost per unit \(average\;fixed\;cost=\frac{Total\;Fixed\;Cost}{Q}\).
  • Note that as \(Q\) increases; the average fixed cost decreases.

• When expanding firms can encounter economies of scale. This means that as inputs double, output increases by more than double.

Questions Which of the following statements is correct?

• If a firm’s technology exhibits constant returns to scale, doubling the inputs leads to doubling of the output level.
  • If a firm’s technology exhibits decreasing returns to scale, doubling the inputs more than doubles the output level.
  • If a firm’s technology exhibits economies of scale, costs per unit will fall as the firm expands its production.
  • If a firm’s technology exhibits diseconomies of scale, doubling the inputs leads to less than doubling of the output level.

4. Production: The cost function for beautiful cars (section 7.3)

• Consider that you own a factory that produces cars. As a factory you will be incuring cost of various kinds.
  • labor, machines, steel, rent
• More cars you produce higher your cost.

Production: The cost function for beautiful cars

Production: The cost function for beautiful cars

• In Figure 4 (previous slide), cost of production increases as you produce more cars.
• In the bottom of Figure 4, average cost \(Average\;cost=\frac{Total\;cost}{Q}\) first decreases and then starts to increase
  • decrease in average cost at first can be because of economies of scale, after a certain point, average cost will begin to increase as resources will have been exhausted.

Production: The cost function for beautiful cars

• Figure 5 shows the marginal cost. At each point on the cost function, the marginal cost (MC) is the additional cost of producing one more unit of output, which corresponds to the slope of the cost function. If cost increases by ∆C when quantity is increased by ∆Q, the marginal cost can be estimated by: \(MC=\frac{\Delta C}{\Delta Q}\).
  • In other words MC is the slope of the Total cost, can one can calculate MC at each quantity of cars \((Q\), by calculating the slope at each point.
  • As the slope of total cost is upward sloping and gets steeper as more cars are produced, marginal cost will increase with \(Q\).
• What is the relationship between AC and MC?
  • It can be seen from Figure 7 (bottom) that as MC increases, AC first falls. But at the segment when AC is falling MC is always below AC. Eventually, as MC keeps rising it will drag the AC upwards.
  • MC intersects AC at the lowest point of AC.

Question 7.5 Choose the correct answer(s)

• Consider a firm with fixed costs of production. Which of the following statements about its average cost (AC) and marginal cost (MC) is correct?

  • When AC = MC, the AC curve has a zero slope.
  • When AC > MC, the MC curve is downward-sloping.
  • When AC < MC, the AC curve is downward-sloping.
  • The MC curve cannot be horizontal.

Question 7.6 Choose the correct answer(s)

• Suppose that the unit cost of producing a pound of cereal is $2, irrespective of the level of output. (This means there are no fixed costs, that is, costs that are present for any level of output, including zero.) Which of the following statements is correct?

  • The total cost curve is a horizontal straight line.
  • The average cost curve is downward-sloping.
  • The marginal cost curve is upward-sloping.
  • The average cost and the marginal cost curves coincide.

5. Demand and Isoprofit

• The demand curve depends on consumer’s willingness to pay. As P increases lower portion of people will be willing to pay for the car (since price is higher), as P decreases more people will be ready to buy the car. This inverse relationship between price and quantity demanded (cars) is known as the law of demand.

Demand and Isoprofit

• Profit: is the difference between firm’s total revenue \(TR\) and total cost \(C(Q)\). \[\begin{align*} \text{profit} &= \text{total revenue} - \text{total costs} \\ &= PQ - C(Q) \end{align*}\]

• it can be written as, \(profit = Q(P-\frac{C(Q)}{Q})\), where \(\frac{C(Q)}{Q}=AC\).
  • note that the shape of the isoprofit curve will depend on the AC.

Demand and Isoprofit

1. The lightest blue curve is the firm’s average cost curve. If P = AC, the firm’s economic profit is zero. So the AC curve is also the zero-profit curve: it shows all the combinations of P and Q that give zero economic profit.
2. Beautiful Cars has decreasing AC when Q < 40, and increasing AC when Q > 40. When Q is low, it needs a high price to break even. If Q = 40 it could break even with a price of $3,400. For Q > 40, it would need to raise the price again to avoid a loss.
3. Beautiful Cars has increasing marginal costs: the upward-sloping line. Remember that the AC curve slopes down if AC > MC, and up if AC < MC. The two curves cross at B, where AC is lowest.
4. The darker blue curves show the combinations of P and Q giving higher levels of profit, so points G and K give the same profit.
5. Profit is higher on the curves closer to the top-right corner in the diagram. Point H has the same quantity as K, so the average cost is the same, but the price is higher at H.

Setting Price and Quantity to Maximize Profit

Setting Price and Quantity to Maximize Profit

• In Figure 8, the profit maximization price at point E. Here, the demand curve is tangential to the darker blue isoprofit curve.
  • P* = $5,440 and Q* = 32
• Also, note that the demand curve is also the feasible frontier. The slope of the demand curve is the marginal rate of transformation (MRT) of lower price into greater quantity sold.

• The isoprofit curve is the indifference curve, and its slope is the marginal rate of substitution (MRS) in profit creation, between selling more and charging more.

• At profit maximization, \(MRT=MRS\).

Question 7.9 Choose the correct answer(s)

• Figure 7.11 depicts the demand curve for Beautiful Cars, together with the marginal cost and isoprofit curves. The quantity-price combination at point E is (Q, P) = (32, 5,440). The average cost of producing 50 cars is the same as the average cost of producing 32. Suppose that the firm keeps the price at P = $5,440 but now produces 50 cars instead of 32. Which of the following is correct?

  • The firm will now sell all 50 cars at $5,440.
  • The firm’s profit will increase.
  • The firm’s profit remains the same.
  • The firm’s profit is now reduced.

Question 7.10 Choose the correct answer(s)

• Figure 7.11 depicts the demand curve for Beautiful Cars, together with the marginal cost and isoprofit curves. At point E, the quantity-price combination is (Q, P) = (32, 5,440) and the profit is $63,360.

Suppose that the firm chooses instead to produce Q = 32 cars and sets the price at P = $5,400. Which of the following statements is correct?

• The profit remains the same at $63,360.
  • The profit is reduced to $62,080.
  • The average cost of production is $3,400.
  • The firm is unable to sell all the cars.

Question 7.11 Choose the correct answer(s)

• Figure 7.11 depicts the demand curve for Beautiful Cars, together with the marginal cost and isoprofit curves.

Suppose that the firm decides to switch from P* = $5,440 and Q* = 32 to a higher price, and chooses the profit-maximizing level of output at the new price. Which of the following statements is correct?

• The quantity of cars produced is reduced.
  • The marginal cost of producing an extra car is higher.
  • The total cost of production is higher.
  • The profit is increased due to the new higher price.

6. Profit maximization using marginal revenue and marginal cost

• In last few sildes, we looked at finding profit maximization price and quantity using the tangential point between the demand curve and the isoprofit line.
• We not look at maximization of profit using marginal revenue (MR) and (MC).
• \(Revenue =Price\times Quantity\), and marginal revenue is the increase in revenue because of increasing quantity from \(Q\) to \(Q+1\).
• The figure below shows calculation of MR when \(Q=20\)

Setting Price and Quantity to Maximize Profit

Q	P	R
Q=20	P=$6,400	R=$128,000
Q=21	P=$6,320	R=$132,720
\(\Delta\)Q=1	\(\Delta\) P=80	\(\Delta\) MR=$4,720

• Note that \(MR=\frac{\Delta R}{\Delta Q}\) as calculated above. MR can also be found by looking at the net of gain and loss. When price moves to $6,320, the revenue from one additional car is $6,320, but there is a loss in the revenue encountered from lowering the price to $6,320 for last 20 cars by $80.
  • Net change in revenue is $6,320 - \(80\)$20=\(4,720\), which is also same as the marginal revenue as calculated above.

Finding profit maximization price and quantity using MC=MR

Figure 10

• In Figure 10, the top figure shows the demand curve. The middle one shows the marginal cost and marginal revenue (Calculated using the demand curve) plotted together. The bottom one shows the profit as a function of quantity.
• it can be seen that profit is the highest when \(MC=MR\). This is because if \(MR>MC\), the firm will increase profit by producing more, and if \(MR<MC\) the firm will increase profit by reducing production. The ideal point is where \(MC=MR\).

Question

• This figure shows the marginal cost and marginal revenue curves for Beautiful Cars. Which of the following statements is correct, based on the information shown?

• When Q = 40, the marginal cost is greater than the marginal revenue so the firm’s profit must be negative.
  • Revenue is greater when Q = 10 than if Q = 20.
  • The firm would not choose to produce at point E because marginal profit is zero.
  • Profit is greater when Q = 20 than when Q = 10.