# 3. Hurley owns a restaurant. To operate the store, he needs to hire labor (L) and...

3. Hurley owns a restaurant. To operate the store, he needs to hire labor (L) and capital (K). The short run production function he is facing is the following: Q(L,K) = 10.5K0.5, where capital is non-adjustable. Moreover, a fixed cost, F, is imposed on Hurley if the restaurant is open. The product's price is p, assumed to be 1. The price of labor and capital are w, and r. We also assume that the market of the restaurant and the labor and capital market is perfectly competitive. Hurley is price taker.
(a) Please write down Hurley's profit. (b) Please solve for Hurley's labor demand. (Express labor demand as a function of wage.) (e) Show that the labor demand is downward slopping. (d) Now, because of COVID-19, delivery service is rising. To adapt to the change. Hurley decides to add delivery service to his restaurant. And in order to do so, Hurley needs to hire another type of labor that only does delivery. Therefore, he is facing a new short run production function Q(Ls, Lp, K) = LLK, where L, is the labor that used in the store, and Lp only does delivery. And K is still non-adjustable. Assuming Hurley cannot switch workers between two different types. Wage for two types of labor is w, wp respectively. And there is also a fixed cost F. Please write down the new profit function for Hurley.

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