# 5 Debbie S Firm Faces The Following Production Function Q K0 5 L 1 0 5a On The Short 2622711

5. Debbie’s firm faces the following production function: q = K0.5 (L-1)0.5a) On the short run, capital cannot be changed and is equal to 25. What will be the cost of producing 25 units, if the rental cost of capital is 20 and the wage is 5?
b) Get the expression for total cost, variable cost, marginal cost, average total cost and average variable cost.Total cost = Variable cost (VC) + Fixed cost (FC)Marginal cost =Average total cost =Average variable cost =c) Graph total cost, variable cost and fixed cost in one graph. Graph marginal cost average cost, average total cost and average variable cost in another graph. TC VC Price
FC
0 QuantityGraph showing total cost, variable cost and fixed cost.
MC ATC AVC Price
0 QuantityGraph showing marginal cost, average total cost and average variable cost.d) At what quantity is the average total cost minimized?
e) What can Debbie do when we get to the long run?
f) What is the MRTS, as a function of K and L?Marginal rate of technical substitution (MRTS) shows the rate at which inputs may be substituted while the level of output remains constant.q = AKa (L)ßMRTS=MPLL/MPLKMPLL= ß AKa (L)ß-1MPLK= a AKa-1 (L)ßTherefore, MRTS= ß AKa (L)ß-1 / a AKa-1 (L)ßMRTS= ß Ka (L)ß-1 / a Ka-1 (L)ßg) Find the long run cost function.