Question

Cafe Caffe sells its product at a price of €5 each (the demand curve is horizontal at this price). Its total and marginal cost functions are: TC = 50 – q +0.01q2 MC = -1 + 0.029, where TC and MC are measured in €, and q is the output rate. (a) Determine the output rate that maximizes profit or minimizes losses in the short run. (b) Calculate the profit earned at the output level you calculated in (a). (c) Suppose that the price of caffe increases to €8, effectively shifting the demand curve up to that level. How does this change Cafe Caffe's optimal output decision? (d) Suppose that workplace safety regulations are imposed that effectively raise the total cost function to: 50 – 9 + 0.02q2. How does the optimal output level change if the output price remains at €5?

Answer 1

TC=50-q +0.01q? MC= .14 0.029 since Demand is horizontal at E 5. Lo, P= MR = d = 5. a) Cuthut which maximises profit in Dhost Run will be determined luy:- MC - MR or -1 +0.02q = 5 : 0.029= 6 9- 6 600 300. 6) Profit earned :- Profit, a = TR-TC fro S Total Revenue? = (p.q)-TC ( Cuantity = 5.9 -(50-9 +0.0193) = 59 - 50+q -0.0192 = ~50 + 6q – 0.01 q ? q= 300 . Now,

- 100 > *= -50 +6(300) - (0.01)(200)? = -50 +1800–00:01)(90000) = -50 + 1800 - 900 = 1800 - 950 > 850, ) Price in Oreased to E8 do MR-8. . MR=MC - 8 = -1 +0.029 ) 9 = 0.029 :: 92 9 900 - 450 F C - q? 0.02 Due to increase in Price, form increases its output to 450 units (d) Change in TC , new TC= 50-q+0.02q² fo, MC = d ((() = -1 + 0.049 - aq s Given in 1 M R = MC Spart (d), that ? price is now 5 31 Do, 5=-1+0.049, At equilibrium. MC

3) 6 = 0.049 2 = 620 - 300 - 50. Due to change in Total Cast, the output change to 150 units.