Final answer:
Charlie will supply in the short run if the price covers his total variable costs, as fixed capital would not affect his decision. His supply decision is impacted by market price and his cost function. Long-run supply decisions will involve adjustments to both capital and labor.
Step-by-step explanation:
The student has asked whether or not Charlie will supply his cattle in the short run if he is operating in a competitive market. To answer this, we consider the economics of Charlie's situation. In the short run, capital (K) is fixed, and the production function is simplified to Q = f[L], reflecting that only labor (L) is variable at this time.
In the short run, if Charlie can cover his total variable costs, he will continue to supply because he would still be contributing to the payment of his fixed costs. However, if the price per head of cattle does not cover the average variable cost, he would minimize his losses by shutting down in the short run. Charlie's decision will depend on the market price (p), his total cost function (C = q² + 10q + 9), and his capacity to produce cattle (q) given his fixed amount of capital.
The long-run considerations differ, as all factors including capital become variable, and Charlie could adjust both labor (L) and capital (K) to find the most efficient production level. In the short run, Charlie will supply in a competitive market. The short run is a period of time when at least one factor of production is fixed, which in this case is capital. Since labor is the only variable factor, Charlie can adjust the quantity of labor he employs to produce more or less cattle. The production function equation q = L⁰.⁵ + K⁰.⁵ indicates that the quantity of cattle produced is dependent on the quantity of labor used.