1. Determining changes in equilibrium price and quantity for a perfectly competitive industry given changes in demand and/or supply (Ch. 2, p. 60-65; Class Notes)
A. Graphical analysis given demand and supply curves
a) While there is increased awareness of Vitamin C available from orange juice, a hard, freezing winter occurs in most of the orange producing areas. Demand increases while supply decreases.
b) While the technology used for tobacco production is improving, there is increased awareness of the health effects of smoking. Supply increases while demand decreases.
c) While there is increased awareness of Vitamin C available from ...view middle of the document...
75 - 0.50)/(0.75 + 0.50)]
= (4/12) / (0.25/1.25) = 1.67.
The arc cross-price elasticity coefficient of 1.67 implies that a one-percent increase in the price of Pepsi would lead to a 1.67 percent increase in the quantity demanded of coke and vice versa, within the price range of $0.50 to $0.75. Thus, Pepsi and coke are substitute goods.
In general, Exy > 0 => goods x and y are substitutes whereas Exy < 0 => goods x and y are complements.
1. Adjusting the quantities of inputs to improve productivity and minimize costs based on the rule for optimal input combination (Ch. 5, 173-175)
When multiple inputs are considered, the rule for optimal input combination is:
MPa/Pa = MPb/Pb = … = MPn/Pn
where MPa, MPb, and MPn are marginal products of inputs a, b, and n whereas Pa, Pb, and Pn are prices of those inputs, respectively.
MPa/Pa measures the units of output per dollar spent on input ‘a.’ Similarly, the ratios for other inputs measure the units of output per dollar spent on each of those inputs. Thus, the rule for optimal input combination is that the units of output per dollar spent on each of the inputs equal to each other.
The MP of an input eventually declines according to the law of diminishing marginal product as the quantity of that input used is increased. Accordingly, the MP curve initially slopes upward, reaches a peak, and then slopes downward when the law of diminishing marginal product is effective. On the downward sloping portion of the MP curve, there is a segment where MP is declining but positive, a point where MP is zero, and finally a segment where MP is declining and negative.
For determining optimal input combination, the decision making segment of the MP curve is where MP is declining but positive. On this segment of the MP curve, there is a negative relationship between the quantity of an input used and its productivity. In other words, if the firm needs to increase the MP of an input, it will use less of the input and if the firm needs to decrease the MP of the input, it will use more of the input. Alternatively, more input means less productivity and less input means more productivity.
Thus, if MPa/Pa > MPb/Pb, the quantity of input ‘a’ should be increased while at the same time decreasing the quantity of input ‘b’. That will decrease the productivity (MP) of input ‘a’ and decrease MPa/Pa while increasing the productivity (MP) of input ‘b’ and increasing MPb/Pb. The process should continue until the use of input ‘a’ has been increased and the use of input ‘b’ has been decreased to the levels at which MPa/Pa = MPb/Pb. The process is reversed if MPa/Pa < MPb/Pb.
MPa/Pa > MPb/Pb also implies that the last dollar spent on input ‘a’ generates a greater return than the last dollar spent on input ‘b.’ Thus, input ‘a’ is a better deal than input ‘b’ and the firm should...