Congratulations you have just completed the purchase of your first company and are now its CEO! Your new firm is a manufacturer of e-bikes and you are now confronted by your company's long-run options for production. You need to build a production facility and you need to choose between two locations: Canada or Mexico. a. Given the available technology, your firm's production function will be q=3LaKb, regardless of where the production facility is located. Find an expression for your firm's MRTS. b. Use whatever method you prefer to find expressions for the cost minimizing levels of L and K. Use your results to write out the firm's long-run cost function [C(w,r,q)]. c. Suppose =32,b=31 regardless of where you locate the plant. If the firm locates in Canada, the firm will have to pay a wage, w=$54, and a cost of capital of r=$125. If it locates the plan in Mexico it would have to pay lower wages, w=$45, but the cost of capital would be higher, r=$169. Given the firm expects to produce 1000 units of output regardless of the location chosen, what are the cost minimizing L and K (it is fine to have fractional units of labor and capital) for each location, and in which country can the firm produce at the lowest cost? Congratulations you have just completed the purchase of your first company and are now its CEO! Your new firm is a manufacturer of e-bikes and you are now confronted by your company's long-run options for production. You need to build a production facility and you need to choose between two locations: Canada or Mexico. a. Given the available technology, your firm's production function will be q=3LaKb, regardless of where the production facility is located. Find an expression for your firm's MRTS. b. Use whatever method you prefer to find expressions for the cost minimizing levels of L and K. Use your results to write out the firm's long-run cost function [C(w,r,q)]. c. Suppose =32,b=31 regardless of where you locate the plant. If the firm locates in Canada, the firm will have to pay a wage, w=$54, and a cost of capital of r=$125. If it locates the plan in Mexico it would have to pay lower wages, w=$45, but the cost of capital would be higher, r=$169. Given the firm expects to produce 1000 units of output regardless of the location chosen, what are the cost minimizing L and K (it is fine to have fractional units of labor and capital) for each location, and in which country can the firm produce at the lowest cost