ECON7790 Assignment 6 Fall 2023 Q1. Suppose a rm produces clothes and requires two input factors: capital and labor. The rm's production function is l 1 f(k,!) 2H!\" where k represents capital input, and 1 represents labor input. Suppose the price per unit of capital and labor is $40 and $10, respectively. a. (20 point) If the rm decides to produce y pieces of clothing, what is the minimum cost to be incurred? b. (5 point)Suppose the rm is in a perfectly competitive product market, how many pieces of clothing should this rm produce if the market price of the clothes it produces is p dollars each? ( hint: the number of clothes is a function of p ) c. (15 point) We further assume that there are 800 rms in that perfectly competitive market, all of which produce the same clothes and all of which have the same production technology, i.e., each of them rm's production Jnction is f(k,l) = k1'"4ll""4 . Meanwhile, the market inverse demand function for the clothes is p : 800 D/ 10, where D denotes the market's demand. Find the market price of the dress when the market is under equilibrium. What is the quantity of clothes sold by each rm? (Hint: the market is under equilibrium when demand = supply)