4. Suppose a competitive firm produces spaghetti dinners. The market price of a

Question

4. Suppose a competitive firm produces spaghetti dinners. The market price of a spaghetti dinner is $20. The cost of making the dinners is given by C(Q) = 10Q + (Q2/160). The marginal cost is given by MC = 10 + (Q/80).

a. How many spaghetti dinners should the firm make each day?
b. What if the firm has avoidable fixed costs of $1562.50?
c. What is the firm's supply function if there is no avoidable fixed cost?
d. What is the supply function if the firm has avoidable fixed costs of $1562.50?

Explanation / Answer

p = $20 C(Q) = 10Q + (Q^2/160) MC = 10 + (Q/80) p = TR -TC TR = 20Q TC = 10Q + (Q^2/160) p = 20Q - [ 10Q + (Q^2/160) ] dp/dQ = 10Q - 2Q/160 profit maxm,dp/dQ = 0 Q = 800. even if there are fixed costs, Q wont change because, Q is derived from MR = MC condition of profit maximisation hence, TFC doesnt matter here. A perfectly competitive firm's supply curve is that portion of its marginal cost curve that lies above the minimum of the average variable cost curve. A perfectly competitive firm maximizes profit by producing the quantity of output that equates price and marginal cost. As such, the firm moves along its positively-sloped marginal cost curve in response to changing prices. VC = 10Q + (Q^2/160) AVC = 10 + Q/160 d(AVC)/dQ = 1/160. it is increasing function. hence, minimum of AVC occurs at origin. supply curve is the MC curve from the origin. fixed costs case: Note: stopping production does not mean going out of business. Ex. Tourist businesses might shut down in the off-season. Why? Whether or not you are producing anything, in the SR, you still have to pay your FC. You should stop producing only if you are losing more money by producing than by shutting down. We need a rule. Let's derive it. Loss > FCTC - Revenue > FCFC + VC - Revenue > FCVC - Revenue > 0 "VC > Revenue That is, shut down if you can't afford to pay your workers. If you shut down, your profit will be negative. But if you shut down, you limit your losses to the amount of FC you have to pay. If VC > Revenue, you'd lose even more than FC by staying open. In general, if you are losing money, you have to decide whether shutting down or staying open will minimize your losses. hence, VC > revenue 10Q + (Q^2/160) > 20Q (Q^2/160) > 10Q Q = 1600 hence, supply curve in this case would be the MC curve from Q = 0 to Q = 1600 only. Please rate life saver! :)

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