question archive Consider an industry of n competitive ?rms
Consider an industry of n competitive ?rms
Subject:EconomicsPrice: Bought3
Consider an industry of n competitive ?rms. For each ?rm, production requires 3 inputs: capital (K), labor (L) and electricity (E). The production function is given by: faces") : Ki (min [L%,E%D. (a) In the short run, capital input is ?xed at K". However, ?rms are free to choose the levels of L and E. Let y denote the output level. Input prices are rug : 2 and wL : 10E : 1. Derive the short—run cost function for an individual ?rm. (1)) In the long run, ?rms can also vary the capital level. Derive a ?rm's optimal choices of K. L and E in the long run. Derive its long—run cost function. Let p be the price of output. Solve for the output supply function and the pro?t function. (c) There are 100 consumers in the economy. Among these consumers= 50 of them have an income of 10 each and the rest have an income of 20 each. Let y denote a consumer's income. For each consumer, the indirect utility function is given by 1; (p13,!) : 51mgr — 21np. i. Solve for the Marshallian demand function for an individual consumer. ii. Calculate the equilibrium market price: p (n). iii. There is an entry fee to this competitive market. (53. Due to the pandemic1 a third of the ?rms have dropped out of the industry. Solve for the number of ?rms currently remain operating.
