Suppose the wage rate is $20 per hour and the rental rate of each unit of capital is $20. The price of output is constant at $80 per unit. Initial capital level is 1 unit. The production function is f(KE) = K1/41/2 a. How much labour should the firm employ in the short run?~ b. How much labour should the firm employ in the long run (Hint: MRS = - 2K/E)?~ c. Find the elasticities of short run and long run labour demand.~ d. According to the theory, which one should have a higher elasticity in absolute terms, short run or long run labour demand? Is your finding in part (c) consistent with the theory?~ e. Find the substitution and scale effects and fill in the table below. Not just with the signs but the actual values of the substitution and scale effects! (Hint: the first step is to calculate the quantity of production after the wage decline)