A firm, which is operating in the conditions of perfect competition, produces good Y. The production function of this firm is y(x) = 20x1/2 , where y denotes the quantity of output Y and x denotes the quantity of input X. Suppose that the price per unit of input X is 120 Euros and the price per unit of output Y is 60 Euros.
a) Find the profit-maximizing level of input and the profit-maximizing level of output for this firm.
b) What is this firm’s profit in case of its profit-maximizing output level?
c) The Government is planning a policy, which envisages simultaneously the following two policies: 1) introduction of a tax of 30 euros per unit of input X (assume that all the economic tax burden will be borne by the users of input X); 2) introduction of a subsidy of 15 euros per unit of output Y (assume that all of the benefit from the subsidy accrues to the producer-supplier of output Y). Find out and justify by calculations, whether this firm would support the planned policy or not? (show calculations for proof, find the profit-maximizing level of input and output and the firm’s profit in case of such policy).