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2.1 Consider the production function: Y=2X + 16X2- 0.4X3 a) Derive marginal value product (VMP) and average value product (AVP) equations. [04] b) At what levels of X do the TPP reach its maximum? [03] c) At what level of X does stage two (II) begin or stage one (I) end? [04] d) Find and interpret elasticity of production (EP) when X = 1. [02]
1.2Suppose that Rose’s monthly income is 200 R/month and she spends her income on two goods: movies and books. The price of movies is Pm=R20 and price of books Pb=R10. Answer the following questions. a) Suppose she spends all her money on these two goods. Draw her budget constraint. Show at least 4 points on this constraint which are attainable (Put books on the horizontal axis). [05] b) Last month she went to movies 5 times and bought 10 units of books. Is this attainable for her? Show it on the figure you sketched in ‘a’. [03] c) Suppose the price of movies increased to R25. Sketch her new budget line. Can you tell from this information how she could allocate her budget between the two goods in order to maximize her utility? Show your workings. [06
1.1 Kagiso has R30 to spend on sugar and salt. Kagiso’s marginal utilities from sugar and salt are shown in the following table. Quantity of sugar MU Quantity of salt MU 1 20 1 40 2 12 2 20 3 9 3 9 4 5 4 7 5 3 5 5 6 1 6 3 i. Suppose that a unit of sugar is priced at R5 and the price of a unit of salt is R10. Compute the weighted marginal-utility for sugar and salt and enter these values in the table. [04] ii. Given Kagiso’s R30 budget, how many units of sugar and salt will be purchased? Explain how you arrived at this answer. [02] iii. Suppose the price of salt stays constant at R10 and the price of sugar falls to R3. How many units of sugar will be demanded at this price? Carefully explain your reasoning. [03] iv. Draw Kagiso’s demand curve for sugar. Does it conform to the law of demand? Why? [02
a populatpion of 1,000 students has an average weekly allowance of =350 and standard deviation of =56.13 .what is the probability that a random sample of size =30 will have an average weekly allowance between 335 and 360?
Pushing over the file cabinet to keep out the
zombies requires 1000 N of force. The cabinet
accelerates at 20 m/s
2
. What is the mass of the
cabinet?
Find the t_a/2 value for a 95% confidence interval when the sample size is 22.
you have been an integer array A of size N.you need to pfint the number with the value closest to zero.if there are multiple elements print the number with greater value.
Consider a sphere of radius R. It is a three-dimensional shape that is bounded by its surface area, a two-dimensional shape. The mathematical equation for the sphere is:
R2 = x2 + y2 + z2. Write the expression for volume (enclosed quantity) and the surface (bounding quantity) of this sphere.
Four electrons are situated at the corners of a rectangle (l=4m; w=2m). Find the resultant force electron A will experience dur to the charges at the other corners of the triangle. The green circle below represents electron A.
Find the electric flux through the left and right sides of an equilateral triangular prism of side 2.00 m when placed in a horizontal unform electric field of 5.0 N/C directed to the right.
#339914 on Dec 2023