Answer to Question #158470 in Microeconomics for Paper boii

Question

4. Define cost and state the type of costs based on production period, and source of cost?

5. Disuse the perfect and imperfect market structures, feature, importance, and limitations of

each market structure from the angle of achieving economic efficiency?

6. Given the demand function Qd=p3, then find the point price elasticity of demand at po?

7. Consider the following short run production function Q = 6L2-0.4L

A) Find the value of L that maximizes output?

B) Find the value of L that maximizes marginal product?

C) Find the value of L that maximizes average product?

8. Given a short run cost function as TC =1/3 Q-2Q2+ 60Q +100, find the minimum value of

AVC and MC?

9. A consumer has birr 600 to spend on the two commodities X and Y, the first commodity X

costs birr 20 per unit and the second commodity Y costs birr 30 per unit .suppose the utility

function given of the consumer is given as U(X,Y)=10X0.60Y0.40

A) Demand for X and Y at optimum respectively?

B) The portion of income that he spends on the consumption of the optimal bundles

X & Y respectively?

10. Suppose a firm faces the production function Q = 0.8 Kº4 L 03. It sells its output at a fixed

price of 450 Birr a unit and can buy K and L at 15 Birr per unit and 8 Birr

per unit

respectively. Then what input mix will maximize profit?

Answer 1

4. Define cost and state the type of costs based on production period, and source of cost?

A cost is the monetary value that has been spent by a company in order to produce a product.

Direct costs are costs that can be traced to a specific object or product. Direct cost may include direct labour and materials.

Indirect costs. These are cost that goes beyond the cost incurred in the creation of a new product. They include the costs involved with maintaining and running a company.

Sources of costs

For direct costs, there are two ways of tracking these costs i.e. the last-in, first-out (LIFO) or first-in, first-out (FIFO). This can be helpful if the costs of your materials fluctuate in the course of production. For indirect costs of indirect costs include administrative expenses and depreciation cost.

5. Disuse the perfect and imperfect market structures, feature, importance, and limitations of

each market structure from the angle of achieving economic efficiency?

Perfect market is a theoretical market structure in which the following criteria are met:

 -All firms sell an identical product (the product is a "commodity" or "homogeneous").

 -All firms are price takers (they cannot influence the market price of their product). Market share has no influence on prices.

-A perfect market has market equilibrium, and an unlimited number of buyers and sellers..

Importance

Perfect markets, though impossible to achieve, are useful because they help us think through the logic of prices and economic incentives. 

 Limitation

Perfect market structures are theoretical assumed which cannot exist in real life. Logical problems arise from the start, especially the fact that it is impossible for any purely competitive industry to conceivably attain a state of equilibrium from any other position. Perfect competition can thus only be theoretically assumed—it can never be dynamically reached.

An imperfect market is an economic market that does not meet the rigorous standards of the hypothetical perfectly—or purely—competitive market.

-In an imperfect market, individual buyers and sellers can influence prices and production.

-There is no full disclosure of information about products and prices, and

-There are high barriers to entry or exit in the market.

Limitation

Not all market imperfections are harmless or natural. Situations can arise in which too few sellers control too much of a single market, or when prices fail to adequately adjust to material changes in market conditions. It is from these instances that the majority of economic debate originates.

6. Given the demand function Qd=p3, then find the point price elasticity of demand at po?

7. Consider the following short run production function Q = 6L2-0.4L

A) Find the value of L that maximizes output?

For max L that maximizes Q

$${\delta _Q\over d_l}=0$$

$$12L-0.4=0$$

$$L=30$$

B) Find the value of L that maximizes marginal product?

$${\delta _Q\over d_l}=0$$

$$12L-0.4=0$$

$$L=30$$

C) Find the value of L that maximizes average product?

$$AP_L={Q\over L}$$

$${6L^2-0.4L}\over L$$

$$6L-0.4$$

$${\delta _Q\over d_l}=0$$

$$L=6$$

8. Given a short run cost function as TC =1/3 Q-2Q2+ 60Q +100, find the minimum value of

AVC and MC?

AVC is at it's minimum when MC =ATC

$$MC={\delta T_c\over d_Q}$$

$$Mc=60.33-4Q$$

$$AT_C={T_C\over Q}$$

$$={1\over 3}+{160\over x}-2x$$

$$MC=ATC$$

$$60.33-4Q={1\over 3}+{160\over Q}-2Q$$

Minimum value of AVC =

$$Q=27.04159$$

9. A consumer has birr 600 to spend on the two commodities X and Y, the first commodity X

costs birr 20 per unit and the second commodity Y costs birr 30 per unit .suppose the utility

function given of the consumer is given as U(X,Y)=10X0.60Y0.40

A) Demand for X and Y at optimum respectively?

$$20x+30y≤600$$

Take Px as the price for x

Py as the price for y

M is the income

The constraint is $\therefore$

$$PxX+PyY=M$$

Derive the langarian function

$$L=10x^{0.4}•y^{0.4}+\lambda(m-PxX-PyY)$$

Partial differentiation of the langarian function

${\delta L\over dx}={{6y^{0.6}}\over x^{0.4}}-px=0$

${\delta L\over dy}={{4y^{0.4}}\over x^{0.6}}-py=0$

${\delta_L\over d_x}=M-p_xx-p_yy=0$

Make lambda the subject

$${={{6y^{0.6}}\over x^{0.4}}\over px}=\lambda={{{4x^{0.4}}\over y^{0.6}}\over py}=0$$

$${3y\over Px}= {2x\over Py}$$

$$y={2xp_x\over 3p_y}$$

$$x={3yp_y\over 2P_y}$$

Substitute the value of xand y into the constraint

$$M=p_x({3yP_y \over 2px})+p_y({2xp_x\over 3py})$$

$$y={mp_x\over 3p_y}$$

$$x={mp_y\over 2p_x}$$