A perfectly competitive firm is trying to adjust to a recent decrease in consumer demand by

adjusting their levels of production. The firm has more than enough existing capital to meet

any reasonable production levels, so must only consider how much labour to hire. Assume

the cost of using this capital is zero. The price of a unit of labour (the wage rate) is ?, the

quantity of labour used is ?, and the price of a unit of output is ?. Labour use is transformed

into output at a rate of ? = ln(?), where ? is the quantity of output.

5. A perfectly competitive rm is trying to adjust to a recent decrease in consumer demand by adjusting their levels of production. The rm has more than enough existing capital to meet any reasonable production levels, so must only consider how much labour to hire. Assume the cost of using this capital is zero. The price of a unit of labour (the wage rate) is w, the quantity of labour used is L, and the price of a unit of output is 3). Labour use is transformed into output at a rate of a: = ln(L), where a: is the quantity of output. (a) TWhat are the rm's total cost, total revenue, marginal cost, and marginal revenue func tions? 'Nhat is the prot maximising level of labour use? How do we know for sure this is the prot maximising level? How does the prot maximising level of labour use change with wages and prices? Write down the indirect prot function of the rm1 and investigate the eifect of increases in p and 10 upon the value of optimal prots. Are the signs of those effects what you would expect? Is the indirect prot function concave, convex or linear in price? Is it concave. convex or linear in the wage rate? From your answers to these questions, can you conclude whether the indirect prot function is concave 0r convex in the vector (p.10)? Assuming that the indirect prot function is convex in the vector (p, to), sketch a contour of the indirect prot function in the space of the output price and the wage rate, and indicate the corresponding better set