"1Answer 1a) Hours Grade in Hours Grade in Total Total hours studiedEconomics studied Mathematics benefitEconomics Mathematics0 70 3 78 148 3 1 77 2 74 151 3 2 82 1 68 150 3 3 85 0 60 145 3 Maximum benefit is obtained when total grade is maximum at 151. Hence Economics should bestudied for 1 hour and Mathematics should be studied for 2 hours.b) i) Income elasticity is defined as % change on quantity demanded / % change in income. Original income (Y) = $15,000Increased income = $60,000Increase in income (?Y) = $45,000 Original consumption of noodle (Qn) = 7 packsNew consumption of noodle 0 packChange in noodle consumption (?Qn) = 0 – 7= -7 Thus, income elasticity of noodle, e = {(45,000/15000) x 100} / -{(7/7) x 100}in= (3 x 100)/(-1 x 100)= -3 2Consumption of movies has increased from 1 to 11 per year.Original consumption movie (Qm) = 1 per yearNew consumption of movie 11 per yearChange in consumption of movie (?Q m) = 11 – 1 = 10Thus, income elasticity of movie, e = {(45,000/15000) x 100} / {(10/1) x 100}im = (3 x 100) / (10 x 100)=3/10=0.3ii) For noodles income elasticity is negative and for movie income elasticity is positive.Thus for the consumer noodle is an inferior good and movie is superior good.iii) Income elasticity measures the responsiveness of a potential buyer to change in income.It shows how the consumption of a consumer changes when income changes, other things(including price of the commodity) remain unchanged. Mathematically income elasticity ofdemand = proportionate change in quantity demanded divided by proportionate change inincome.It is true that more consumption is always preferred to less consumption. But in case ofinferior good the consumer diminishes purchase of inferior good and increases purchase ofsuperior good which s/he was unable to afford previously, but can afford after increase inincome. Inferior goods have negative income elasticity. iv) As the economy enters into recession, income level falls. People will have less money tospend on costly superior goods. In the given example, movie is superior good and noodle is 3inferior good. Thus as income falls demand for movie tickets will fall and demand fornoodle will rise. Thus revenue of movie operator will fall and revenue of seller of noodlewill rise. Answer 2a) Quantity TUMU TU MU MU / P MU / Pf f b b (fish) (fish) (bread) (bread)0 00 1 200 200 140 140 200/10=20 140/10=142 360 160 260 120 160/10=16 120/10=123 500 140 360 100 140/10=14 100/10=104 620 120 440 80 120/10=12 80/10=8Price of fish and of bread per unit is $10, and budget of the consumer is $40Thus P = $10, P= $10f b And P * Q + P * Q = $40 (Budget line).f f b b Applying rational spending rule, total utility is optimized when, MU / P = MU / P = MU per dollarf f b bThe above condition is satisfied for 3 units of fish and 1 unit of bread where MU / P = MU /f f b P = 14.bThus the consumer can maximize total utility by purchasing 3 units of fish and 1 unit ofbread. Total utility derived by the consumer is 500 + 140 = 640. 4Figure 1The Rational Spending Rule: Spending should be allocated across goods so that themarginal utility per dollar is the same for each good. Combination of fish and bread that cost $40 Total utility 0 units of fish + 4 units of bread 0 + 440 = 4401 unit of fish + 3 units of bread 200+360=5602 units of fish + 2 units of bread 360 + 260 = 6203 units of fish + 1unit of bread 500 + 140 = 6404 units of fish + 0 units of bread 620+0=620b) i) Demand function P = 60 – 5Q, P = $40Price elasticity of demand (e ) = dQ/dP * P/Q p5P = 60 – 5QOr, 5q = 60 – PPutting P = 40,5Q = 60 – 40Or, 5Q= 20Or, Q= 20/5 = 4Thus Q = 4, P = 40.0 0 5q = 60 – POr, Q = -P/5 + 60/5Differentiating Q wrt P,dQ /dP = -1/5 + 0 = -1/5Thus e = -1/5 * 40/4 = -1/5 * 10 = -2 = 2 (negative sign ignored).pii) Price elasticity of demand is a very important tool in deciding upon product pricing by acompany. Price elasticity can range from 0 to infinity. At 0 it is perfectly inelastic, at infinityit is perfectly elastic, from 0 – 1 it is inelastic, at 1 it is unit elastic, and for more than 1 it iselastic.In the instant case price elasticity is 2 that is elastic. This means increase in pricewill lead to more than proportionate fall in demand. Thus the company is not expected toearn more revenue by increasing price, rather revenue will fall.iii) Total revenue is P * QR = P * Q 62 R = (60 – 5Q) * Q = 60Q – 5QAt maximum total revenue, first order derivative of total revenue with respect to Q is 0. dR/dQ = 60 – 10Q = 0?Q = 60/10 = 6Putting the value of Q in the demand function we getP = 60 – 5*6 = 60 – 30 = 30Thus revenue maximizing price is $30.Answer 3a) Price is $6. Since the firm is operating in perfectly competitive market, P = AR = MR =$6. Equilibrium of a perfectly competitive firm is achieved at the equality of MR and MC. Asper the given diagram, equilibrium quantity is 600 units at AC $4. Thus profit per unit is $6- $4 = $2. Total profit then comes to $2 * 600 = $1200A firm will shut down even in the short run if price falls below the minimum point of theaverage variable cost. So long as price is more than the minimum average variable cost(AVC), the firm need not shut-down. So long as price> minimum AVC, the firm is fullycovering the variable cost and part of the fixed cost. When P = minimum AVC, the firmrecovers the variable cost fully, but fixed cost remains un-recovered. Still the firm need notshut down, as the variable cost is being recovered. But if P<minimum AVC the firm is not ina position to even cover the variable cost fully. In this situation the firm should shut-downas at this price the variable cost is not recovered fully. Thus the minimum AVC is the shutdown point.7At P = $6 the price is well above the minimum AVC which is $2.5. Hence in the short-run itis in the interest of the firm to operate at this price.b) At P = $3, the firm is incurring loss as the AC>P (AR).But P ($3) > minimum AVC (2.5).Hence the firm should operate instead of shutting down as the firm is still capable ofrecovering the total variable cost at this price. The actual loss cannot be determined as the co-ordinate of the corresponding point on ACcurve cannot be ascertained from the given diagram.c) At P = $1, price falls below the minimum AVC and the firm is not in a position to evenrecover the variable cost. Hence it is in the interest of the firm to shut-down even in theshort-run. d) Point ‘A’ is the minimum point of the MC curve. Marginal cost is the addition to total costcaused by very small increment in output.It may be defined as change in total cost as aresult of unit change in output. MC initially falls due to efficient use of variable factors andreaches minimum (point A in the diagram).As production increases further, outputinterferes with the efficient use of variable factors and the MC starts to rise. Point ‘B’ is the minimum point of the AVC curve. AVC first falls due to operation ofeconomies of scale, and reaches minimum point (‘B’ in the diagram). As output furtherincreases, diseconomies of scale set in and AVC starts rising.“B” is also shut-down point inthe short-run, as if price falls below ‘B’, the firm is unable to recover even variable costsand must shut-down to avoid further loss. 8Point “C” is the minimum point of AC curve.AC falls initially as both AVC and AFC fall, andafter reaching the minimum pint it increases as though AFC falls but rising AVC more thanoutweigh falling AFC. In the long run, equilibrium of a perfectly competitive firm is established at the minimumpoint of the AC through which MC passes and intersects with MR (P = AR). Thus “C”represents long-run equilibrium of the firm. Answer 4a) Revenue maximizing price and quantityRevenue (R) = P * Q2 R = (24 – Q) *Q = 24Q – Q [Given P = 24 – Q]Max R => dR/dQ = 0dR/dQ = 24 – 2Q = 0? 24 = 2QOr, Q =24/2 = 12Putting the value of Q in P = 24 – Q, we getP = 24 – 12 = $12 Thus revenue maximizing price and output are $12 and 12 units respectively.b) Profit maximizing price and quantityProfit (?) = TR – TC2 TR = 24Q – Q9TC = 6Q [Given AC = $6]2 2 ? ? = TR – TC = 24Q – Q - 6Q = 18Q – QMax ? => d?/dQ = 0Differentiating ? w.r.t. Qd?/dQ = 18 – 2QSetting d?/dQ = 018 – 2Q = 0? 2Q = 18Or, Q = 18/2 = 9Putting the value of Q in P = 24 – Q, we getP = 24 – 9 = $15Thus profit maximizing price and quantity are $15 and 9 units respectively. 10Figure 2Equilibrium of monopolist Cost & Revenue MC p r 15 AC t s 9 0 Output MR A R Profit = the areaprst Please refer to the above figure. S is the point of equilibrium, where minimum AC = MC =$6.At the left of S MR>MC, so there is scope to increase profit by increasing output. Beyond SMC>MR, so the firm’s profit starts to fall. Hence maximum profit is the area prst = (15- 6)*9 = $81c) Imposition of tax on the producer "