Suppose Krazy Kokonut is the sole producer of coconut wine on the island of Some

Question

Suppose Krazy Kokonut is the sole producer of coconut wine on the island of Somewhere. The inverse demand function for KK wine is: P = 1000 - 1Q - .2 I, where P is price per bottle, Q is bottles of wine, and I is per capita income in Somewhere . Marginal costs of producing wine are positively related to Q. That is, the higher is Q, the greater is MC. If per capita income in Somewhere goes up, what happens to the profit-maximizing level of production of KK’s wine and the price of wine? Explain carefully.

Explanation / Answer

Given that Krazy Kokonut is a monopolist of coconut wine.

The inverse demand function is: P = 1000 - 1Q - .2I. Rearrange this to find the demand function as:

Q = 1000 - 1P - 0.2I

Marginal costs of producing wine are positively related to Q. in a way such that the higher is Q, the greater is MC.

Note that the income is negatively related to the consumption of wine, the income elasticity is negative (sign of - 0.2). This means wine is an inferior good. When the per capita income in Somewhere goes up the demand for wine will go down and hence, the demand curve will shift to the left. Unwillingly, the monopolist have to reduce the production of Q since Marginal revenue will also shift to the left.

Thus, the profit-maximizing level of production of KK’s wine will fall and along with it the price of wine falls too.

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