ECON 431 Midterm: ECON 431 Cal Poly SLO 2009 Midterm Solutions
Document Summary
Round off values to one decimal place where necessary. Consider a negative externality situation in which a firm emits air pollution that harms consumers breathing the air as a result of using a chemical solvent (x). The firm"s production function is y = f(x) = 10x 0. 2x2, where x is the amount of solvent the firm uses. The input price of solvent is v = and demand for the firm"s output is infinitely elastic at p=. = pf(x) - vx = 10(10x 0. 2x2) 20x = 100x 2x2 20x. Foc: d /dx = 100 4x 20 = 0. Note: environmental damages as a function of x are: d(z) = d(2x) = 4(2x) + (2x)2. So that, mec per unit of x is mec = 8 + 4x. Welfare (w): w = pf(x) vx d(z) = - d(z) = 100x 2x2 20x 8x 2x2. Verify that the input tax you calculated leads the firm to use x* units of solvent.
