# DSE 2012- Question 16,29 and 30.

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## DSE 2012- Question 16,29 and 30.

 I'll post the following questions here. I somehow couldn't wrap my head around them. Any help regarding how to go about solving it and so on, would be greatly appreciated. 30) Suppose that there are two agents in an economy with income x1 and x2. If the richer person transfers a portion of her income to the poorer person without changing the income ranking (that is the rich remains richer even after the transfer) then it is called a progressive transfer. Welfare of this economy is measured by a function W(x1; x2). W is a `good' measure of social welfare if the social welfare increases due to a progressive transfer. Consider the following candidates for W; W1(x1; x2) = x1 + x2 W2(x1; x2) = x1x2 (a) Only W1 is a `good' measure (b) Only W2 is a `good' measure (c) Both W1 and W2 are `good' measures 29) The demand curve for electricity is D(p) = 120  p. The marginal cost of electricity production is MC1(q) = 20 + q. The marginal cost of pollution due to electricity production is MC2(q) = 3q. Find the competitive equilibrium output and the social optimum output. (a) 50; 20 (b) 50; 30 (c) 60; 20 (d) 60; 30 16) The equation x^7 = x + 1 (a) Has no real solution (b) Has no positive real solution (c) Has a real solution in the interval (0; 2) (d) Has a real solution but not within (0; 2)
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## Re: DSE 2012- Question 16,29 and 30.

 Q.16).Ans: Try to plot the fn graph (i.e x^7-x-1=0) you will see that there is a real sol. in the interval (0,2) Q.29).Ans: a)Competitive equilibrium output: D(p)=120-p or D(q)=120-q(i.e inverse demand fn) Now solve: D(q)=MC1(q), You will get q=50. b)Social optimum output: solve D(q)=MC1(q)+MC2(q) you will get Q=20. So the answer is option-A(50;20) Note: we add MC2 in part-B coz we taking this cost is bearing by society. Q.30).suppose that X1=richer person in the economy X2=poorer person in the economy. Now, suppose income of X1=5 and X2=2 which means total income of two person in the economy=X1+x2=7. from this we get W1(x1; x2) = x1 + x2=7 W2(x1; x2) = x1*x2=10 Now, suppose due to progressive transfer the new income of two is X1=4 and X2=3(Note: the total income in the economy is still the same and the rich remains richer even after the transfer) Now If we check welfare given by above 2 equation after progressive transfer we will get W1(x1; x2) = x1 + x2=7 W2(x1; x2) = x1*x2=12 The above result clearly shows that Only W2 is a `good' measure bcoz it increases social welfare which is not the case in W1.. So, answer is b).Only W2 is a `good' measure M.A Economics Delhi School of Economics 2013-15 Email Id:sumit.sharmagi@gmail.com
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## Re: DSE 2012- Question 16,29 and 30.

 can u do this one ? give d steps only . Suraksha’ is the sole producer and supplier of security systems in India and the sole employer of locksmiths in the labour market. The demand for security systems is D( p ) = 100 − p , where p is the price. The production of security systems only requires locksmiths and the production function is given by f ( L) = 4 L , where L is the number of locksmiths employed. The supply curve for locksmiths is                                                   given by L( w) = max    0, w/2-20 , where w is the wage rate.                                     24. How many locksmiths will ‘Suraksha’ employ?        a) 5       b) 10      (C) 15       d) 20 25. If the government sets the minimum wage is 70 , how many locksmiths will Suraksha employ?          a)            5          b)            10          c)            15          d)            20
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## Re: DSE 2012- Question 16,29 and 30.

 In reply to this post by Sumit 16 ) how do we plot d graph in one variable case ?/
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## Re: DSE 2012- Question 16,29 and 30.

 In reply to this post by maahi I was trying to solve both of them by simply putting MR=MC..but I'm not getting the answer..even I'm unable to get any given option provided in questions..How was u trying it???? M.A Economics Delhi School of Economics 2013-15 Email Id:sumit.sharmagi@gmail.com
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## Re: DSE 2012- Question 16,29 and 30.

 In reply to this post by maahi Like we do in other polynomial function such as quadratic, X^3 , X^4 etc. M.A Economics Delhi School of Economics 2013-15 Email Id:sumit.sharmagi@gmail.com
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## Re: DSE 2012- Question 16,29 and 30.

 In reply to this post by Sumit i still don't get d graph part . i tried finding optimal input by equating marginal revenue product of d factor to wage and then substituted d found expression in d profit function of d monopolist
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## Re: DSE 2012- Question 16,29 and 30.

 In reply to this post by Sumit i got d ans for 1 . mr = 100-2q, output is a function of L i.e y= q=4L substitute this in MR. compute MRP (L) = MR *MP(l) and equate it to w . u get 10 point something and 10 is d answer .
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## Re: DSE 2012- Question 16,29 and 30.

 In reply to this post by maahi q16) x^7-x-1=0 as the eqn is of 7th order..so it will hav 7 roots...complex roots occurs in pair..so if the eqn has 6 complex roots..than for sure one of the root is real.and using a good approximation of around 1.1 its directs towards option c. else newton raphson method can be used .
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## Re: DSE 2012- Question 16,29 and 30.

 In reply to this post by Sumit Thanks a lot :) I couldn't get the graph part though :s
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## Re: DSE 2012- Question 16,29 and 30.

 In reply to this post by wolverine how to come about that approximation ?
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## Re: DSE 2012- Question 16,29 and 30.

 In reply to this post by Sumit I have a slight doubt @sumit. Dont we multiply q to the inverse demand function to make it total revence (price x qty=TR) and then differentiate it to get MR. Next step would be to equate it to MC and find the q. while you have directly equated the MC to inverse function.  your ans is absolutely right and I am getting wrong ans by the method i just pointed out. But is there a mistake in that approach??