Microeconomics Answers

. The market demand and supply for the good are given as Qd = 250 - 50P and Qs = 25 + 25P; A) Find the equilibrium price and quantity respectively B) Calculate the price elasticity of demand at equilibrium point. C) Calculate the price elasticity of supply at the equilibrium point. D) What is surplus or shortage if price is Birr 5

. Assume in a market individual firm supply function of a commodity X is given by Sx=-10 + 4Px and individual demand function is Dx =6 -2Px. There are 10 suppliers of commodity X with identical supply function and there are 100 buyers of the commodity X with identical demand function. Find market equilibrium price and quantity demanded.

Suppose a small country produces only food and clothing. A new agricultural technology is then introduced that doubles the amount of food that can be produced per year.

Use the​ 3-point-curve drawing tool to draw a new production possibilities boundary on the graph on the​ right, labeled​ b, reflecting the change in the agricultural technology. Properly label this line. Place end points one on horizontal and one on vertical axes.

Kumar spends all his monthly income of $20 on two goods, rice (x) and cooking oil (y). The price of oil is $1 per liter. Rice can be purchased at a government-run store and also on the free market. The price of rice is $1 per kilogram at the government store but he can only buy up to 10 kgs. In the free market, the price of rice is $2 per kg. Draw Kumar’s budget constraint assuming that the goods are divisible

Suppose the relationship between the government’s tax revenue (T) and national income (Y) is represented by the equation T= 25+0.75Y. Plot this relationship on a scale diagram, with Y on the horizontal axis and T on the vertical axis. Interpret the equation.

Use the line drawing tool to draw the equation. Make sure to plot the vertical axis as one endpoint of the line. Properly label this line.

Kumar spends all his monthly income of $20 on two goods, rice (x) and cooking oil (y). The price of oil is $1 per liter. Rice can be purchased at a government-run store and also on the free market. The price of rice is $1 per kilogram at the government store but he can only buy up to 10 kgs. In the free market, the price of rice is $2 per kg. Draw Kumar’s budget constraint assuming that the goods are divisible.

 Find derivatives of the following functions:

• y=(4x+3)/ln[2x2 +3x−5] • y=3(e2x +e−2x)(x2 −4)

here are 5,000 identical individuals in the market of commodity X, each with a demand function given by Qdx = 6 - P, and 1,000 identical producers of commodity X, each with a function given by Qsx = 10P, where Qdx is an individual's quantity demanded, Qsx is a single producer's quantity supplied, and Px is the price of the commodity.

a. Find the market demand function (QDx) and the market supply function (QSx) for commodity X.

b. Determine the market demand schedule and the market supply schedule of commodity X (for whole dollar prices) and from them find the equilibrium price and the equilibrium quantity.

c. Plot, on one set of axes, the market demand curve and the market supply curve for commodity X and show the equilibrium point.

d. Obtain the equilibrium price and the equilibrium quantity mathematically.

e. Explain why the equilibrium condition is considered stable.

f. Determine the elasticity of demand for commodity X at the equilibrium point.

6. Find the maximum and minimum values of the following functions

a) 3X4 -X3 +2

b) x4 – 14x2 +24x +9

7. Find the profit maximizing output given Q = 200 – 10p and AC = 10 + Q25 where Q is quantity, p is price and AC is average cost.

8. Find the first order and second order partial derivatives of the following function

a) Z = 2x3 +5 x2y +xy2 +y3

b) Z = log (x2 + y2)

9. Find elasticity of demand if demand function is x = 250 – 5p +p2. Also find elasticity of demand at p = 8

10. Find elasticity of demand if demand function is p = 50 – 3q. Also find elasticity of demand at p = 5

Suppose that the manager of a firm is planning to meet an order of 1000 units of two products X and Y. The manager's problem is to find the combination of two goods that minimize its cost. He has the firm's cost function of two goods estimated as

C = 5X2 + 20 Y2

By using the Lagrangian multiplier method, find the quantity of X and quantity of Y, subject to X + Y = 1000, that minimize the cost of meeting the order.