An exercise: I want you to work through these global equations for corn supply and demand

Background Information

ln Qs=4.3561 + (0.2*ln P) + (0.015*t)

• This is a supply equation. Qs and P are in natural logs (the ln operator).
• The coefficient on P is therefore price elasticity of supply, set equal to 0.2.
• t is a time trend, set equal to 0 in 2020 and 30 in 2050 (that is, t increases by 1 each year). It captures productivity growth in corn production. You should interpret the coefficient on t (0.015) as indicating that Qs increases by 1.5% per year for any given P.

ln Qd= -2.0520 - (0.2*ln P) + (0.5*ln Y) + (1.0*ln Pop)

• This is a demand equation for corn; the variables are all in natural logs (the ln operator)
• Qd is quantity demanded, P is price, Y is per capita income, and Pop is population.
• The coefficient on P is the price elasticity of demand ( -0.2 ), while that on Y is the income elasticity of demand ( 0.5 ). It is assumed that increases in population add proportionately to demand (1% increase in Pop leads to 1% increase in demand).

Data: see the values below for the initial year in 2020, and for four different 2050 scenarios

	2020	2050a	2050b	2050c	2050d
Q	100	?	?	?	?
Y	100	143	143	156	156
Pop	100	125	125	135	135
t	0	30	30	30	30
productivity	0.015	0.015	0.005	0.015	0.005

• Data: Q, Y and Pop are all expressed in index numbers, such that 2020 values for each are set to 100, and later years give values relative to 2020.
• Thus a value of 143 in 2050a means that Y is 43% greater than in 2000 (you then need to take the natural log of 100, or the relevant Index number value, in calculations.

The Question

1.

a. Solve for price (P) in 2020. That is, convert the 2020 values for Q, Y, and Pop to natural logarithms. Then set ln Qs= ln Qd, and solve for ln P. Then convert ln P to its antilog, P.

*You should get a value of $3.50

b. Use the values for 2050 A, 2050B, 2050C, and 2050 D in the table. Solve for price in each case.

Note that the coefficient on t (productivity growth) is reduced to 0.005 from 0.015 in 2050B and 2050D.

c. Briefly summarize your findings. In particular, discuss the role of productivity growth in meeting future demand needs