Production economics questions.

The derived demand curve is;

1. The portion of the average cost curve where the slope is positive
2. The portion of the marginal revenue curve where the slope is positive
3. The portion of the marginal cost curve above the variable cost curve
4. None of the above is true.

A farmer at Mikese Morogoro establishes that during the last year tomato production was such that the marginal revenue was higher than marginal cost. The farmer should;

1. Reduce the level of fixed variable inputs to reduce production cost
2. Reduce the level of fixed variable inputs to reduce production cost
3. Increase the level of inputs up to the optimum level
4. Set a higher price for the product to increase total revenue

A producer is a price taker in the factor market because;

1. Their demand for inputs is too small to influence the market price
2. They are too many to compete
3. They produce according to the law of supply and demand
4. They are rational producers

Given the total cost function 120Y-Y² +0.002Y³ . Where Y is output. If the product price is 200SHS, the producer is not making any profit because;

1. The marginal revenue is lower than the average total cost
2. The marginal revenue is equal to minimum average variable cost
3. The product price is lower than the minimum average total cost
4. None of the above is true

For producer with the production function;

Y=2X+2X²-0.4X³ where X=input and Y=output ; Unitary elasticity of production is attained as the coordinates (x,y)

1. (10,210)
2. (25,675)
3. (20,220)
4. None of the above is true.

Write short notes with illustration(mathematical or graphical) to indicate whether each of these statements is true or false.

1. In a perfectly competitive market, the least cost condition is sufficient for profit maximization
2. The minimum long run average variable cost is equal to the short run average cost of the least  efficient firm size.
3. Returns to scale is synonymous to economiies of size
4. The law of diminishing returns is used to plan production levels in the long run.

Consider the production function;

If the product price is 1000 SHS and the factor prices are P_x1=50SHS and P_x2=100

1. Find the equation representing the isoquant family of curves
2. Find the equation for the expansion path
3. Find the equation representing the isoclines family of curves
4. What is the optimum combination of inputs?

Derive the criteria for optimum allocation of a bundle of resources when you have to produce more than one product.

1. Illustrate graphically and discuss the needed resource adjustment in order to achieve the maximum secondary product wheni.

Where X₁ and X₂ are resources; and Y₁ and Y₂ represent the same products produced from two different units. P_x1 and P_x2 and P_y1 and P_y2  and P_Y2 are the factor and product prices respectively.

2. Illustrate graphically and discuss the required resource adjustment in order to achieve the maximum secondary product when;

Basic economic principles show that for profit to be maximized there must be optimum allocation of resources as guided by the equi-marginal value product criteria;

1. Does this creteria account for resources constraints? Explain
2. A firm manager is required to maximize production subject to resource constraints as follows:

subject to

1. Compute the optimum combinations of inputs
2. Compute the shadow price of each of resource in physical terms
3. What is the interpretation of the shadow price?
4. Why is constrained optimization necessary in production economics?