1. Given the following production function

a) Calculate the APP,  MPP and elasticity of production at different production levels.

b) How many stages of production does this function represent? Mention them.

c) Between which levels of fertilizer would you advise a farmer to operate rationally?

d) Give an intuitive reason why you would advise a farmer to operate rationally in the stage you said in (c) above

e) Assume two factors of production are competing in a production process. Explain how a decrease in the price of one input may result in an increase in the market price of the other input.

2. a) Differentiate an isoproduct from an isoquant map. Illustrate the difference and also explain the characteristics underlying an isoquant.

b) For the following quadratic production function for production of an output Y, using two variable inputs, X₁ and X₂ : Y=18X₁-X₁²+14X₂-X₂² derive the isoquant equation for this production function by solving for X₁. Show your work clearly and do not omit important steps.

c) Derive the marginal criterion for profit maximization for a farm business as a function of output. Explain each of the terms in the marginal criterion you have derived

d) Explain the difference between factor-product relationship and product-product relationship.

3. a) Explain who a peasant farmer is and explain any two peasant household models. Elaborate on the relevance of farm mechanization to a peasant farmer.

b) Explain the following concepts and illustrate them graphically.

i) Isoquants.

ii) Ridge lines.

iii) Expansion path.

iv) Technical complements.

On 15^th October, 2008, a three day workshop took place in Sinazongwe district to train farmers on efficient resource allocation in agriculture. A small sample of farmers was trained so that they could extend the knowledge learned to others. Other issues discussed included use of a new technology in agriculture called conservational tillage, economic efficiency and elasticity of production. The overall objective of the workshop was to indirectly help improve productivity so as to reduce food insecurity among the farmers in the area. Following that event, a survey among Sinazongwe farmers was carried out five months later to determine their understanding of resource use. Most of them argued that there is no need to expand the total planted area of maize.

One of the surveyed people, the Donoso Co-operative chairman of the same district suggested that in order to feed the rising population in Sinazongwe district, farmers should just be encouraged to apply increasing quantities of fertilizer on existing cultivated fixed amount of land.

Q.1.

a) Using illustrations, discuss your position by arguing for or against the Donoso Co-operatives chairman's statement. You may illustrate your position diagrammatically if necessary.

b) One of the surveyed farmers in the same district, Mr Wabule grows maize. He comes to you complaining that he did not fully understand how he could achieve economic efficiency at his farm with two inputs, land and fertilizer. Advise him as an agricultural economist on how he can achieve economic efficiency given his factor-factor relationship condition he is in.

3. You are a manager of Mana farm and have been tasked to determine how much maize and wheat can be produced with different types of nitrogen (N). The following are the production functions for maize (M) and wheat (W).

M=65.54+1.084N_M-0.003N²_M and W=68.07+0.830N_W-0.002N²_W where N_M is nitrogen used in maize production in kg and N_W is nitrogen used in wheat production in kg. You have 100kg of nitrogen available for 2hactares of land, one for maize and the other for wheat. The following prices are prevailing in the market; Pm-maize price=K3 per kg, Pw-wheat price=K2 per kg.

a) How much of Nm and Nw can you advise to use?

b) How much M and W will be produced from the levels of nitrogen in (a)?

c) Determine the value marginal products of the two enterprises.

d) What happens to the value marginal products when nitrogen is increased from 100 to 200kg?

e) Is it true that the value marginal product in stage two of production is the demand curve for an input? Explain.

4. Define technology and explain its relevance to agriculture. Explain the types of technology that are widely used in agriculture and their relevance to Zambia.

5. What is agricultural policy? Does Zambia have an agricultural policy currently? If yes, what major areas does it touch? If no, what would you advise the government as a policy maker? Why? Give any two examples of non-price agricultural policy instruments used in Zambia.