Question

In: Economics

1) The Demand and Supply Functions of a two-commodity market model are as follows: Qd1 =...

1) The Demand and Supply Functions of a two-commodity market model are as follows:

Qd1 = 10 - 2P1 +P2

Qs1 = -2 + 3P1

Qd2 = 15 + P1 - P2

Qs2 = -1 + 2P2

a. Find Pi* and Qi* (i = 1, 2). (Use fractions rather than decimals).

b. Based on this two-commodity model, what can you infer about the relationship between good 1 and good 2?

c. What is the economic meaning of the coefficient of P1 in the equation Qd1 = 10 - 2P1 + P2

Solutions

Expert Solution

a. Equilibrium occurs when Qd = Qs
At i = 1, Qd1 = Qs1 gives,
10 - 2P1 +P2 = -2 + 3P1
So, P2 = 3P1 + 2P1 -2 -10
So, P2 = 5P1 - 12

At i = 2, Qd2 = Qs2 gives,
15 + P1 - P2 = -1 + 2P2
So, 2P2 + P2 = 15 + P1 + 1
So, 3P2 = 16 + P1
So, 3(5P1 - 12) = 16 + P1 (as P2 = 5P1 - 12)
So, 15P1 - 36 = 16 + P1
So, 15P1 - P1 = 16 + 36
So, 14P1 = 52
So, P1* = 52/14 = 3.71

So, P2* = 5P1 - 12 = 5(3.71) - 12 = 18.55 - 12 = 6.55

Q1* = -2 + 3P1 = -2 + 3(3.71) = -2 + 11.13 = 9.13

Q2* = -1 + 2P2 = -1 + 2(6.55) = -1 + 13.1 = 12.1

b. We can find the cross price elasticity of demand to find the relationship between good 1 and good 2.
Cross price elasticity of demand of good 1 with respect to price of good 2, e =

From demand equation,

So, e = (1)*(6.55/9.13) = 0.72
As cross price elasticity is positive so good 1 and good 2 are substitutes.

c. Coefficient of P1 in the equation Qd1 = 10 - 2P1 + P2 is -2. This means that as price of good 1 increases by 1 unit then quantity demanded of good 1 decreases by 2 units.

Rahul Sunny answered 2 years ago
Next > < Previous

Related Solutions

1. Market demand and supply for a commodity are given by the following equations: Demand: X...
1. Market demand and supply for a commodity are given by the following equations: Demand: X = 30 – (1/3) P Supply: X = -2.5 + (1/2) P where X= quantity (units), and P=price per unit ($) Suppose that the government is planning to impose a tax on this commodity and considering the following two options: Option 1: A unit tax of $15 Option 2: An ad valorem tax of 20% a) Find the tax incidence on buyers and producers,...
1.Suppose the commodity demand functions in two separate markets are as follows:    Q1=500-3P1 and      Q2=500-2P2...
1.Suppose the commodity demand functions in two separate markets are as follows:    Q1=500-3P1 and      Q2=500-2P2 and a monopoly can cater to these markets at a constant marginal cost of $2. a. Calculate the profit-maximizing quantities of output supplied to the two markets, their prices and the total profits reaped by the monopoly b. Calculate the deadweight losses associated with this practice of third degree price discrimination; c. Suppose the monopoly now resorts to a single-pricing policy. What would then...
Market demand and supply for a commodity are given by the following equations: Demand: X =...
Market demand and supply for a commodity are given by the following equations: Demand: X = 30 – (1/3) P Supply: X = -2.5 + (1/2) P where X= quantity (units), and P=price per unit ($) Suppose that the government is planning to impose a tax on this commodity and considering the following two options: Option 1: A unit tax of $15 Option 2: An ad valorem tax of 20% a) Find the tax incidence on buyers and producers, and...
The demand and supply functions for corn are as follows. The quantity is in thousands of...
The demand and supply functions for corn are as follows. The quantity is in thousands of bushels and the price is in dollars per bushel. QD = 1000 – 100 P QS = - 245 + 90 P A. What are the equilibrium price and equilibrium quantity in this market? Round your answers to 2 decimal places. B. Graph this market and label all relevant points (equilibrium points, intercepts, axis labels, etc.). C. Calculate the consumer surplus at the equilibrium...
Consider a market with demand and supply functions: Supply function: ? = 40? − 40 Demand...
Consider a market with demand and supply functions: Supply function: ? = 40? − 40 Demand function: ? = 200 − 20� a. Find deadweight loss of the price floor. [Hint: Deadweight loss is a region lost because of no trade.] Welfare effects of a tax Now, the government repeals the price floor and imposes a sales tax of $3 per good on buyers-side. b. Draw a new demand curve with old demand and supply curves. Find the new equilibrium...
The Market Forces of Supply and Demand (Continued from Q1) Consider two functions: Supply function: ?...
The Market Forces of Supply and Demand (Continued from Q1) Consider two functions: Supply function: ? = ? + 5 Demand function: ? = 20 − 4? a. For some reasons (e.g. wage level rises), the supply decreases. Note that it means the supply curve shifts to the left. More precisely, consider the quantity supplied decreases by 5 units for each price level. Write down a new supply function and draw a graph of the new supply curve and demand...
Let the demand and supply functions for a commodity be Q =D(P) ∂D < 0 ∂P...
Let the demand and supply functions for a commodity be Q =D(P) ∂D < 0 ∂P Q=S(P,t) ∂S>0, ∂S<0 ∂P ∂t where t is the tax rate on the commodity. (a) What are the endogenous and exogenous variables? (b) Derive the total differential of each equation. (c) Use Cramer’s rule to compute dQ/dt and dP/dt. (d) Determine the sign of dQ/dt and dP/dt. (e) Use the Q − P diagram to explain your results. Find the Taylor series with n...
Let the demand and supply functions for a commodity be Q =D(P) ∂D < 0 ∂P...
Let the demand and supply functions for a commodity be Q =D(P) ∂D < 0 ∂P Q=S(P,t) ∂S>0, ∂S<0 ∂P ∂t where t is the tax rate on the commodity. (a) What are the endogenous and exogenous variables? (b) Derive the total differential of each equation. (c) Use Cramer’s rule to compute dQ/dt and dP/dt. (d) Determine the sign of dQ/dt and dP/dt. (e) Use the Q − P diagram to explain your results. Find the Taylor series with n...
1.     The market demand and supply functions for toothpaste are: Qd = 12 - .04P and...
1.     The market demand and supply functions for toothpaste are: Qd = 12 - .04P and Qs = 3.8P + 4 a.     Calculate the equilibrium quantity and price and point elasticity of demand in equilibrium. b.     Next, calculate consumer surplus. Suppose the toothpaste market is taxed $0.25 per unit. c.      Calculate the revenues generated by the tax. d.     Calculate the loss in consumer surplus. What percentage of the burden of the tax is paid for by consumers?
Industry demand and supply functions for potatoes are as follows:             QD = -1,450 – 25P...
Industry demand and supply functions for potatoes are as follows:             QD = -1,450 – 25P + 12.5PW + 0.1Y             QS = -100 + 75P – 25PW – 12.5PL + 10R Where: Q is number of potato bushels (in millions). P is the avg. wholesale price of potatoes (in $/bushel). PW is avg. wholesale price of wheat (in $/bushel), estimated to be $4. Y is annual income (GDP in $ billions); estimated to be $15 trillion. PL is avg....
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT