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)

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.

Suppose a firm has its TR and TC functions estimated as follows:

TR = 300Q-3Q2

TC = 500 + 50Q + 2Q2

Find (a) profit function of the firm, (b) the quantity of output (Q) that maximizes the firm's profit.