Question #85132

If the demand curve is Q(p) = p^a (where a < 0), what is the elasticity of demand? If the marginal cost is $2, and a = -4, what is the profit-maximising price?

Consider an example of the third degree price discrimination. There are two groups of consumers. Consumers are identical within each group. In group 1, the demand function is P = 6 - 3Q, in group 2, the demand function is P=5-2Q. The marginal cost of production is 1. Find out the optimal price for each group.

Consider an example of the third degree price discrimination. There are two groups of consumers. Consumers are identical within each group. In group 1, the demand function is P = 6 - 3Q, in group 2, the demand function is P=5-2Q. The marginal cost of production is 1. Find out the optimal price for each group.

Expert's answer

If the demand curve is Q(p) = p^a (where a < 0), then the elasticity of demand is Ed = a*p/Q.

If the marginal cost is $2, and a = -4, then the profit-maximising price is P = MR = MC = $2.

In group 1, the demand function is P = 6 - 3Q, in group 2, the demand function is P = 5 - 2Q. The marginal cost of production is MC = 1. The optimal prices for each group are:

1) if P = 6 - 3Q, then MR = TR' = (P*Q)' = 6 - 6Q.

The optimal quantity at MR = MC is:

6 - 6Q = 1,

Q = 5/6 units, P = 6 - 3*5/6 = $3.5.

1) if P = 5 - 2Q, then MR = TR' = (P*Q)' = 5 - 4Q.

The optimal quantity at MR = MC is:

5 - 4Q = 1,

Q = 1 unit, P = 5 - 4*1 = $1.

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