One convenient way to express the willingness-to-pay relationship between price

Question

One convenient way to express the willingness-to-pay relationship between price and quantity is to use the inverse demand function. In an inverse demand function, the price consumers are willing to pay is experessed as a function of the quantity available for sale. Suppose the inverse demand function (expressed in dollars) or a product is P = 80 - q, and the marginal cost (in dollars) of producing it is MC = 1q, where p is the price of the product and q is the quantity demanded ad/or supplied.

a) How much would be supplied in a static efficient allocation?

b) What would be the magnitude of the net benefits (in dollars)?

Explanation / Answer

P = 80 - q

MC = q

(a) Allocation is efficient when profit is maximized by equating price with MC.

80 - q = q

2q = 80

q = 80/2 = 40

So, 40 units will be supplied.

(b)

When q = 40, P = 80 - q = 80 - 40 = 40

Total revenue (TR) = P x q = 40 x 40 = 1600

Total cost (TC) = q x MC = q x q = 40 x 40 = 1600

Net benefit = TR - TC = 1600 - 1600 = 0

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