4. Consider an industry of at competitive rms. For each rm, production requires 3 inputs: capital (K), labor (L) and electricity (E). The production function is given by: l l l f(K,L,E) = K: (min [L3,EID. (a) In the short run, capital input is xed at K\". However, rms are free to choose the levels of L and E. Let 3; denote the output level. Input prices are mg 2 2 and 11),; = mg 2 1. Derive the short-run cost function for an individual rm. (b) 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 prot 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 v (p,y) = 51113; 2lnp. 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, 4!). Due to the pandemic, a third of the rms have dropped out of the industry. Solve for the number of rms currently remain operating