University:
University of Michigan
Course:
ECON 613 | Advanced Topic in Mathematics for Economists
Academic year:

2024
Views:

431

Pages:

2
Author:

Alvinska H.

Sales Subsidies in Economics: Contribution to Market Prices Name: Alvinska Hebat Grade: 910-Math Sales Subsidy Effect If a producer is given a sales subsidy by the government, the effective ability of the producer to bid for the goods he sells will increase. Therefore, the price of subsidized goods will be cheaper than unsubsidized goods. If the producer's supply function: P = a + mQ and if the government subsidizes the sale of Rp s, per unit of goods offered then the producer supply function after the subsidy is: P = a + mQ-s where P = price / unit; Q = quantity of goods offered s = subsidy per unit of goods Example: The market for good X has the following market demand and supply functions: Demand Function (Dd): P = 28 - 1.6Q Supply Function (Ss): 2P = 1.6Q + 8 or P = 4 + 0.8Q If the producer of the good is given a government subsidy of Rp 1.20, the supply function after the subsidy is : P = f(Q) - S or P = 0.8Q + 4 - 1.20. The market equilibrium after the subsidy is: Demand = Supply 28 - 1.6Q = 0.8Q + 4 - 1.20 resulting in Q = 10.5 and P = 11.2. So after a sales subsidy to producer X of Rp 1.20 per unit of X sold, the equilibrium price now falls from Rp 12 per unit to Rp 11.2 and the equilibrium quantity rises from 10 units to 10.5 units. Change of Direction Coefficient on Linear Functions In functions that have a positive directional coefficient: Y = f(X) = a + mX Equation (1) where Y,X = variables; a = constant; m = direction coefficient = ΔY/ΔX. } If there is an increase in the direction coefficient "m" by Δm, then equation (1) changes to: Y' = a + (m + Δm)X, so the direction coefficient of the new function is now: m+Δm } If there is a decrease in the direction coefficient "m" by Δm, equation (1) becomes: Y" = a + (m - Δ m)X, so the direction coefficients of the new function are now: m - Δm } When there is an increase in the direction coefficient, the Yo line will shift to Y'; while decreasing the direction coefficient, the Yo line will shift to Y". } At the same price of Y in Yo then: an increase in the direction coefficient causes the value of X to decrease from X0 to X', and a decrease in the direction coefficient causes the value of X to increase from X0 to X". In functions that have a negative direction coefficient: Y = f(X) = a - mX Equation (2) where Y, X = variables; a = constant; m = direction coefficient = ΔY/ΔX. } If there is an increase in the direction coefficient "m" by Δm, then equation (2) above changes to : Y' = a - (m + Δm)X, so the direction coefficient of the new function is now : (m + Δm). } If there is a decrease in the direction coefficient "m" by Δm, the above equation becomes as follows Y" = a - (m - Δm)X, so the direction coefficient of the new function is now as follows: (m - Δm). } When there is an increase in the direction coefficient, the Yo line will shift to Y'; while decreasing the direction coefficient, the Yo line will shift to Y". } At the same price of Y in Yo then: an increase in the direction coefficient causes the value of X to decrease from X0 to X', and a decrease in the direction coefficient causes the value of X to increase from X0 to X". Conclusion: an increase in direction coefficient always corresponds to the steepness of a line; and a decrease in direction coefficient always corresponds to the slope of a line.