Q#1 (40 marks) Suppose the firm's production function is given as Q = 10KL, where L is labor, K is capital. 1) Calculate the elasticity of substitution of this production function. (5marks ) 2) What is the equation of the isoquant corresponding to this production function? (5marks ) 3) What type of return to scale does this production exhibit? And Why? ( 5marks ) 4) Derive the long run total cost function. (5 marks) 5) What is the long run average and marginal cost functions? (5 marks) 6) Suppose that capital is fixed at a level K . What is the short run total cost function for this production function. (5 marks) 7) What is the short run average variable cost and short run average fixed cost functions? (5 marks) 8) Suppose that the price of labor w=$5 and the price of capital r =$20. What is the cost- minimizing input combination if the firm wants to produce 50 units? ( 5 marks) Q#2 (15 marks) A consumer buys two goods, good X and a composite good Y. The utility function is given as U(X, Y) = In3XY. The price of X is Px, the price of Y is Py and Income is I. 1) Derive the demand equation for good X. ( 5 marks) 2) Are the two goods X and Y complements or substitutes? Why? ( 5 marks) 3) Suppose that I=$10 and suppose that initially the Px = $1 and subsequently Px falls and becomes $0.5 per unit. Calculate numerically the value the price effect as a result of the drop in Px and graph the results. (5 marks)g 3 {15 marks) Suppose all firms in the market are identical. Each rm has a long run total cost curve LTC 2 300 Q2 + 0.0103. The market demand curve is Q = 25,000 1000;\". Find the long run equilibrium quantity per firm, price, and number of rms in the market