Question

the inverse demand function for good X is P = 5−0.05Q. The firm’s cost curve is TC(Q) = 10+Q

If the monopoly could engage in perfect price discrimination,

(1.26) (2 points) What are the total variable costs at the profit maximizing level of output? (1.27) (2 points) What is the value of consumer surplus at the profit maximizing level of output? (1.28) (2 points) What is the value of producer surplus at the profit maximizing level of output?

Answer 1

Answer 1.26

(i)

Perfect price discrimination is also known as first degree price discrimination in which producer charges price according to their consumers maximum willingness to and hence If consumers maximum willingness to pay is greater than or equal to Marginal Cost(MC) of producing then it will sell to that consumer and charges its maximum willingness to pay.

Hence It will produce that quantity at which P = MC

MC = dTC/dQ = 1

Hence P = MC => P = 5−0.05Q = 1 => Q = 80.

Variable cost is the portion of cost which depends on output. Here part of TC which depends on output(Q) is +Q.

Hence Total Variable cost = Q = 80

Hence Total Variable cost = 80

(ii)

Consumer surplus is the surplus or benefit consumer receives by paying price less than what they are willing to pay. As monopolist is charging price equal to their maximum willingness to pay. Hence there is no benefit or surplus to the consumers.

Hence Consumer surplus = 0

(iii)

Fixed cost is the portion of cost which is constant and does not depends on output. Here part of TC which does not depends on output is 10

Hence Total Fixed cost = 10

Producer surplus = TR - TC + Fixed Cost (In the short run)

Total Cost = 10 + 80 = 90

TR is the total area below demand curve (because of first degree price discrimination

=> Producer surplus = TR - 10 - Q + 10 = TR - Q
Hence Producer surplus is the area below demand curve and above MC curve

Here Y intercept = 5

Hence Producer surplus = (1/2)(5 - 1)80 = 160.

Hence Producer surplus = 160