Question in computer science sir solve this problem and provide me correct solution I$\text{'}$m in very hurry...

Question $1$ Consider the following production function:

$y=F(L,K)=4L^{\frac{1}{}}{K}^{\frac{1}{b}}$

where $L$ and $K$ are the amount of labour and capital used in the production process, and $y$ is the output. Throughout this question, the output price $p$ is $3$ and the rental rate of capital $r$ is $1.$

We will first consider a firm in the short run, where the amount of capital is fixed at $K=64.$ The fixed cost is therefore $64.$

$($a$)($Level A$)$ Is there diminishing returns to labour? Explain.

$($b$)($Level A$)$ Suppose the wage rate $w$ is $1.$ Find the profit$-$maximising choice of $L.$ Calculate the profit$-$maximising output level and the maximised profit. $($There is no need to check the second order condition $-$ but of course you can check if you want to$.)$

$($c$)($Level A$)$ Now suppose $w$ increases to $2.$ Find the profit$-$maximising choice of $L.$ Calculate the profit$-$maximising output level and the maximised profit. $($There is no need to check the second order condition.$)$ You can leave your answers in square roots.

$($d$)($Level A$)$ What is the change in $L$ when $w$ increases from $1$ to $2$ in the short run? You can leave your answers in square roots.

Question $2[36$ marks$]$

A mass of consumers is uniformly distributed along the interval $0,1.$ Two firms, A and $B,$ are located at points $0$ and $1$ respectively. We denote by $p,$ the price of firm iinA,$B.$ A consumer located at point xin$[0,1]$ obtains utility $U_A(x)=u-p_A-t{x}^2$ if he consumes from firm $A,$ and $U_B(x)=u-p_y-t(1-x{)}^2$ if he consumes from firm $B.$ In the following, we assume that the groes utility $u$ is sufficiently high, so that the market will be covered and all consumets will get positive utility in equilibrium. Both firms have a cost function equal to $T_i(q_1)=(1+x)q_i,$ where you should substitute $x$ for the last number of your student ID number.

$($a$)$ Find the demand function for both firms.

$[5$ marks$]$

$($b$)$ Assume firms set their prices simultaneously. Solve for the Nash equilibriura prices, and compute the equilibrium profits.

$[6$ marks$]$

$($c$)$ Now, assume a Stackelberg timing, where firm A is the leader. Explain briefly why we should not use the Nash equilibrium concept to solve this game, and solve for the equilibrium prices and profits.

$[8$ marks$]$

$($d$)$ Compare the results obtained in parts $($b$)$ and $($c$)$ and explain the intuition for such difference Are the equilibria efficient?

marks$]$

$($e$)$ Suppose that there was a technology that allowed firm A to credibly commit not to change its price $($this option to commit would make firm A the Stackelberg leader, as in part c$).$ If only firm A had access to this technology, how much would firm A be willing to pay for it$?$ How would your answer change if the technology was auctioned to the best bidder $($between firms A and $B?$

$[4$ marks$]$

Assume that firms A and $B$ can perfectly discriminate between locations. That is$,$ firm i chooses a prioe $p_1(x)$ for each location xin$[0,1].$ Firms now compete by simultaneously choosing the pricing functions $p_1()$ and $p_2().$ There is no possibility of arbitrage, and if a consumer may be indifferent between firms A and $B,$ they go to the closest firm.

$($f$)$ Find the Nash$-$equilibrium pricing functions. That is$,$ you need to find the equilibrium prices of every firm in every location.

$[8$ marks$]$

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Question In Theory of Compilers

Q$1$ generate target code for the following source language statements :

Solve it like this Example

target code for the assignment statement $d$:$=(a-b)+(a-c)+(a-c)$ can be translated into the foll sequence of three address code:

Three Address Code:

$\backslash$table$[[$Statement$,$Code Generated,$\backslash$table$[[$Re