--%>
Assignment Help - homework help

Market demand function

The market  for good X consists  of 2 consumers. consumer  1',s demand  for good X is:

X1 :  15 - 3Px + 0.5PY + .02I1

I1 and I2 are incomes of consumer 1 and 2, respectively.  Px and Py are the prices of goods X and Y, respectively.

a. What is the equation  for the market  demand  function  for X? Graph the two individual demand curves and the market  demand  curve  for the case which  I1 : $2000, I2: $3000, and Py:$ 10.

b. Suppose Px rises  from $5 to $5.05. What is the market price elasticity of demand?

c. Suppose  income  is redistributed so that each consumer  has $2500. If Px: 5 and Py: 10, how much does the quantity of X demanded  change because  of the redistribution?

E

Expert

Verified

a) Equation for consumer 1: X1= 15-3Px + 0.5 Py +0.2I1

Equation for consumer2:  X2= 15-3Px + 0.5 Py + 0.2 I2

Market demand curve is  calculated by aggregating the individual demand curves.

So, By adding the two demand curves we get:  X*=30-6Px +Py + 0.2I1+ 0.2I2

Put the value of Py and I1 and I2.

X*= 30 -6Px + 10 + 0.2(2000) + 0.2(3000) is the market demand curve for the good X

Individual Demand curves will be:

X1= 15-3Px +5 + 400 or X1= 420-3Px
X2= 15-3Px+ 5 +600 or X2= 620-3Px
X*= 30-6Px + 10+ 1000 or X*= 1040-6Px

b. For market   price  elasticity we use market demand curve:

X*= 1040- 6Px

Elasticity:
dx/dp(p/x)=
dx/dp= -6
-6(5/1010)=-0.029

P= original price-which is 5(that is price before the price change)
X= orginal  quantity: quantity demanded at original price of 5= 1040-6(5)=1010
And dx/dP=slope of market demand curve

c. Now each consumer has 2500. So, Put the values In the market demand curve:

X*= 2040-6Px
If Px=6
Then X* demanded will be 2004
And Earlier it would be: X*= 1040-36= 1004
So the change in quantity demanded will be: 1000

   Related Questions in Microeconomics

  • Q : Determine unskilled labor for minimum

    A minimum legal wage of $5 per hour in this market for unskilled labor would: (w) have no effect on employment or the wages paid. (x) create new jobs for 3,000 unskilled workers. (y) move some low-skilled workers above the poverty line. (z) create une

    		•
  • Q : LEAST affected labor in short run The

    The short-run demand for labor would be LEAST affected by the: (w) productivity of the resource. (x) prices of substitute resources. (y) demand for goods produced by the resource. (z) fixed costs of a firm. Hey fri

    		•
  • Q : Asymmetric information Provide the

    Provide the solution of this question. The problem of asymmetric information is that: A) neither health care buyers nor providers are well-informed. B) health care providers are well-informed, but buyers are not. C) the outcomes of many complex medical procedures cannot be predicted. D) insurance co

    		•
  • Q : Loss in social welfare with quantity

    When pharmaceutical manufacturers conspire to generate only Q1 penicillin, in that case the: (i) purely-competitive firms which produced penicillin would experience economic losses. (ii) resulting excessive antibiotic treatments would produce strains of dru

    		•
  • Q : Constant shortages of a good problem

    Constant shortages of a good are nearly always attributable to: (1) legal ceiling prices which are set beneath equilibrium. (2) Recessions which yield maximum unemployment rates. (3) Price gouging by firms through monopoly power. (4) Legal price floor

    		•
  • Q : Reducing proportion of the work force

    The assertion which unions are more powerful nowadays than ever before is: (i) Supported by the consequences of the union contracts on an inflationary spirals. (ii) Reflected in the growing proportion of workers included in violent, protracted and costly strikes. (iii

    		•
  • Q : Problem on Determinants of Demand I

    I have a problem in economics on Determinants of Demand. Please help me in the following question. Income and tastes most directly influence the: (i) Demand. (ii) Market equilibrium (iii) Prices. (iii) Quantities. (iv) Supply.

    Q : Centers for production in circular flow

    I have a problem in economics on Centers for production in circular flow model. Please help me in the following question. The centers for production in a circular flow model are termed as: (1) Households. (2) Public enterprises. (3) Business firms. (4

    		•
  • Q : Creating unhealthy dependency by

    According to several critics who favor reducing welfare payments, and existing welfare programs as: (1) cannot cure poverty without substantial funding hikes. (2) are justified only when they increase total production. (3) harm poor people by creating

    		•
  • Q : Determine demands for relatively price

    When technological advances within agriculture generate bumper crops of farm products for that demands are relatively price inelastic, in that case the: (w) average income of farmers will decline relative to per capita income for the

    		•