IGNOU BECC-102 December 2021 Previous Year Question Paper

Q1.(a) Show that when profit is maximised, where € a= elasticity of demand.

(b) A firm has a demand and total cost function given by the respective equations P=300-—Q and TC = 800 +2Q. Find the price, quantity and ¢ q at which profit is maximised.

Q2.The demand and supply functions for a good at time t are given as: 00६ 5 125 - 27,

Q3.,5-50 + 1-57, 1

(a) State the equilibrium condition, hence deduce a difference equation in P.

(b) Solve the difference equation to find the equilibrium price and quantity.

Q4.(a) Find the gradient of the line 2x - 3y +1 =0 and the coordinates of the points where it cuts the axes.

(b) Show that the line joining the points (p, q) and (kp, kq) passes through the origin, whatever the values of p, q and k.

Q5.(a) The supply and demand functions for a product are : qs = p?— 400, and qq = P? — 40p + 2600 Determine the market equilibrium price and quantity.

(b) The demand function for a particular product is q = f(p) = 2400 — 15p, where q is stated in units and p in rupees. Determine the revenue function. What is the total revenue when the price is = 50 ? What is the quantity demanded at this price ? At what price is the total revenue maximised ?

Q6.Capital K and Labour L in an economy are given by the linear functions K=24+38t, L=1+4t, where t denotes time. Find the rate of change with respect to time.

Q7.If the marginal revenue function is MR = _ab - ९, show that p = _ab_ —cis the demand function. Here p is price and x is quantity demanded. पर. Discuss the basic set-up of the Cobweb model.

Q8.(a) Suppose A = {x, y, z}. List all the subsets of

(b) What is an injective function ?

(c) What do you understand by Cartesian product ?

Q9.(a) Explain the following : @ Theorem Gi) Proof

(b) Briefly discuss the various types of proof.

Q10.Examine the continuity of the functions : (1-52) y 1-x

(b) y=x(x+1), for x>0