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2. (3 points) Consider a company that provides lawn-care services where Q denotes the number of maintained lawns, N denotes the number of laborers, and
2. (3 points) Consider a company that provides lawn-care services where Q denotes the number of maintained lawns, N denotes the number of laborers, and K denotes the number of lawn mowers (per day). Each laborer can only use one lawn mower and can maintain 5 lawns per day. Therefore, this company's production technology can be expressed as Q5min{N,K}. Denote the price of lawn-care services as p. a) (1 point) Suppose it cost $100 to rent a lawn mower and $100 to hire a laborer per day. What is the cost-minimizing input combination (N,K) in order to maintain 50 lawns in a day? Graphically illustrate how (N,K) is derived by drawing the isocost line and the isoquant. b) (2 points) Now, suppose that the cost to rent a lawn mower drops to $75. Conditional on maintaining the same total cost level as in part (a), what is the firm's profit-maximizing quantity of lawns maintained? Graphically illustrate how the new optimum is found by drawing the isocost line and the isoquant. Graphically depict the magnitude of the substitution and scale effects. 2. (3 points) Consider a company that provides lawn-care services where Q denotes the number of maintained lawns, N denotes the number of laborers, and K denotes the number of lawn mowers (per day). Each laborer can only use one lawn mower and can maintain 5 lawns per day. Therefore, this company's production technology can be expressed as Q5min{N,K}. Denote the price of lawn-care services as p. a) (1 point) Suppose it cost $100 to rent a lawn mower and $100 to hire a laborer per day. What is the cost-minimizing input combination (N,K) in order to maintain 50 lawns in a day? Graphically illustrate how (N,K) is derived by drawing the isocost line and the isoquant. b) (2 points) Now, suppose that the cost to rent a lawn mower drops to $75. Conditional on maintaining the same total cost level as in part (a), what is the firm's profit-maximizing quantity of lawns maintained? Graphically illustrate how the new optimum is found by drawing the isocost line and the isoquant. Graphically depict the magnitude of the substitution and scale effects
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