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What is the MC of producing an additional engine and the MC of each lawn tractor

1. A company has developed the production function of Q=80 L^(0.5) K^(0.6) where L represents labour and K represents capital.
a. If L is increased by 2% with K unchanged, what is the resulting percentage change in output?
b. Describe the nature of returns to scale for this production function.

2. A firm makes and sells lawn tractors. The sum of the costs of frames, assembly and the engine equals the cost of each tractor. The firm produces its own engines according to the cost equation CE=235,000+800Q+3Q^2. The cost of the frames and assembly is $550 per lawn tractor. The demand function is Q=320-0.04P.
a. What is the MC of producing an additional engine and the MC of each lawn tractor? Find the firm’s profit-maximizing quantity and price.
b. Assume the firm has the chance to buy an unlimited number of engines from another company at a price of $845 per engine. Will this option affect the number of lawn tractors the firm plans to produce? What would their price be? Will the firm continue to produce its’ own engines? If so, how many?

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