A company gets a contract to do one simple job to validate tickets at the entrance...

 

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A company gets a contract to do one simple job to validate tickets at the entrance of a theme park. The output of this company is q, which measures how many tickets have been validated in one hour. The inputs are K and L. K represents the tickets validated by machine. L represents the tickets validated by workers. The rent the company needs to pay for each ticket validated by the machine is r and the wage for each ticket validated by workers is w. The production function is q = K + L. 120. Indicate clearly the values (a) Draw the isoquant map for qi = 100 and 92 of the intercepts. (b) Suppose the company has already signed a contract to employ the machine for validating 50 and only 50 tickets in one hour. Calculate the (short-run) total cost of fulfilling the two output targets, q₁ = 100 and q2 = 120. (c) Now, suppose the contract above has expired and the company can freely employ any quantities of K and L. Draw a diagram to indicate the cost-minimization points for the targets q = 100 and 92 = 120. Please consider two scenarios: when r> w and when r < w. (d) Given what you have done in (c), try to derive the (long-run) total cost function (a function relating total cost to total output), average cost function (a function relating average cost to output) and marginal cost function (a function relating marginal cost to output). Assume input prices are unchanged with output. Consider two scenarios: r> w and r<w. (e) Is the total cost in (b) higher or lower than that in (d) for the two output targets? P (f) Does the cost structure exhibit economies or diseconomies of scale, or no scale effects? [You should show it mathematically.] A company gets a contract to do one simple job to validate tickets at the entrance of a theme park. The output of this company is q, which measures how many tickets have been validated in one hour. The inputs are K and L. K represents the tickets validated by machine. L represents the tickets validated by workers. The rent the company needs to pay for each ticket validated by the machine is r and the wage for each ticket validated by workers is w. The production function is q = K + L. 120. Indicate clearly the values (a) Draw the isoquant map for qi = 100 and 92 of the intercepts. (b) Suppose the company has already signed a contract to employ the machine for validating 50 and only 50 tickets in one hour. Calculate the (short-run) total cost of fulfilling the two output targets, q₁ = 100 and q2 = 120. (c) Now, suppose the contract above has expired and the company can freely employ any quantities of K and L. Draw a diagram to indicate the cost-minimization points for the targets q = 100 and 92 = 120. Please consider two scenarios: when r> w and when r < w. (d) Given what you have done in (c), try to derive the (long-run) total cost function (a function relating total cost to total output), average cost function (a function relating average cost to output) and marginal cost function (a function relating marginal cost to output). Assume input prices are unchanged with output. Consider two scenarios: r> w and r<w. (e) Is the total cost in (b) higher or lower than that in (d) for the two output targets? P (f) Does the cost structure exhibit economies or diseconomies of scale, or no scale effects? [You should show it mathematically.]

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a Isoquant Map The production function is q K L which represents a straightline isoquant with a slope of 1 To draw the isoquant map we need to find di... View the full answer